Combinatorial Constructions In Ergodic Theory And Dynamics

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Combinatorial Constructions in Ergodic Theory and Dynamics

Author : A. B. Katok
Publisher : American Mathematical Soc.
ISBN 13 : 0821834967
Total Pages : 127 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Combinatorial Constructions in Ergodic Theory and Dynamics by : A. B. Katok

Download or read book Combinatorial Constructions in Ergodic Theory and Dynamics written by A. B. Katok and published by American Mathematical Soc.. This book was released on 2003 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ergodic theory studies measure-preserving transformations of measure spaces. These objects are intrinsically infinite, and the notion of an individual point or of an orbit makes no sense. Still there are a variety of situations when a measure preserving transformation (and its asymptotic behavior) can be well described as a limit of certain finite objects (periodic processes). The first part of this book develops this idea systematically. Genericity of approximation in various categories is explored, and numerous applications are presented, including spectral multiplicity and properties of the maximal spectral type. The second part of the book contains a treatment of various constructions of cohomological nature with an emphasis on obtaining interesting asymptotic behavior from approximate pictures at different time scales. The book presents a view of ergodic theory not found in other expository sources. It is suitable for graduate students familiar with measure theory and basic functional analysis.

Hyperbolic Dynamics, Fluctuations and Large Deviations

Author : D. Dolgopyat
Publisher : American Mathematical Soc.
ISBN 13 : 1470411121
Total Pages : 354 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hyperbolic Dynamics, Fluctuations and Large Deviations by : D. Dolgopyat

Download or read book Hyperbolic Dynamics, Fluctuations and Large Deviations written by D. Dolgopyat and published by American Mathematical Soc.. This book was released on 2015-04-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the semester-long special program on Hyperbolic Dynamics, Large Deviations and Fluctuations, which was held from January-June 2013, at the Centre Interfacultaire Bernoulli, École Polytechnique Fédérale de Lausanne, Switzerland. The broad theme of the program was the long-term behavior of dynamical systems and their statistical behavior. During the last 50 years, the statistical properties of dynamical systems of many different types have been the subject of extensive study in statistical mechanics and thermodynamics, ergodic and probability theories, and some areas of mathematical physics. The results of this study have had a profound effect on many different areas in mathematics, physics, engineering and biology. The papers in this volume cover topics in large deviations and thermodynamics formalism and limit theorems for dynamic systems. The material presented is primarily directed at researchers and graduate students in the very broad area of dynamical systems and ergodic theory, but will also be of interest to researchers in related areas such as statistical physics, spectral theory and some aspects of number theory and geometry.

Geometric and Probabilistic Structures in Dynamics

Author : Keith Burns
Publisher : American Mathematical Soc.
ISBN 13 : 0821842862
Total Pages : 358 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric and Probabilistic Structures in Dynamics by : Keith Burns

Download or read book Geometric and Probabilistic Structures in Dynamics written by Keith Burns and published by American Mathematical Soc.. This book was released on 2008 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents a collection of articles that cover areas of mathematics related to dynamical systems. The authors are well-known experts who use geometric and probabilistic methods to study interesting problems in the theory of dynamical systems and its applications. Some of the articles are surveys while others are original contributions. The topics covered include: Riemannian geometry, models in mathematical physics and mathematical biology, symbolic dynamics, random and stochastic dynamics. This book can be used by graduate students and researchers in dynamical systems and its applications."--BOOK JACKET.

Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby

Author : Joseph Auslander
Publisher : American Mathematical Soc.
ISBN 13 : 1470422999
Total Pages : 336 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby by : Joseph Auslander

Download or read book Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby written by Joseph Auslander and published by American Mathematical Soc.. This book was released on 2016-11-29 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of three conferences in Ergodic Theory and Symbolic Dynamics: the Oxtoby Centennial Conference, held from October 30–31, 2010, at Bryn Mawr College; the Williams Ergodic Theory Conference, held from July 27–29, 2012, at Williams College; and the AMS Special Session on Ergodic Theory and Symbolic Dynamics, held from January 17–18, 2014, in Baltimore, MD. This volume contains articles covering a variety of topics in measurable, symbolic and complex dynamics. It also includes a survey article on the life and work of John Oxtoby, providing a source of information about the many ways Oxtoby's work influenced mathematical thought in this and other fields.

Polynomial Methods in Combinatorics

Author : Larry Guth
Publisher : American Mathematical Soc.
ISBN 13 : 1470428903
Total Pages : 287 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Polynomial Methods in Combinatorics by : Larry Guth

Download or read book Polynomial Methods in Combinatorics written by Larry Guth and published by American Mathematical Soc.. This book was released on 2016-06-10 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.

A Vision for Dynamics in the 21st Century

Author : Danijela Damjanovic
Publisher : Cambridge University Press
ISBN 13 : 1009278878
Total Pages : 446 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis A Vision for Dynamics in the 21st Century by : Danijela Damjanovic

Download or read book A Vision for Dynamics in the 21st Century written by Danijela Damjanovic and published by Cambridge University Press. This book was released on 2023-12-31 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: A large international conference celebrated the 50-year career of Anatole Katok and the body of research across smooth dynamics and ergodic theory that he touched. In this book many leading experts provide an account of the latest developments at the research frontier and together set an agenda for future work, including an explicit problem list. This includes elliptic, parabolic, and hyperbolic smooth dynamics, ergodic theory, smooth ergodic theory, and actions of higher-rank groups. The chapters are written in a readable style and give a broad view of each topic; they blend the most current results with the developments leading up to them, and give a perspective on future work. This book is ideal for graduate students, instructors and researchers across all research areas in dynamical systems and related subjects.

Handbook of Dynamical Systems

Author : B. Hasselblatt
Publisher : Elsevier
ISBN 13 : 0080533442
Total Pages : 1231 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Dynamical Systems by : B. Hasselblatt

Download or read book Handbook of Dynamical Systems written by B. Hasselblatt and published by Elsevier. This book was released on 2002-08-20 with total page 1231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volumes 1A and 1B.These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys.The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics.Volume 1B will appear 2005.

Conformal Dimension

Author : John M. Mackay
Publisher : American Mathematical Soc.
ISBN 13 : 0821852299
Total Pages : 162 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Conformal Dimension by : John M. Mackay

Download or read book Conformal Dimension written by John M. Mackay and published by American Mathematical Soc.. This book was released on 2010 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this concept has proved extremely fruitful in a diverse range of areas, including geometric function theory, conformal dynamics, and geometric group theory. This survey leads the reader from the definitions and basic theory through to active research applications in geometric function theory, Gromov hyperbolic geometry, and the dynamics of rational maps, amongst other areas. It reviews the theory of dimension in metric spaces and of deformations of metric spaces. It summarizes the basic tools for estimating conformal dimension and illustrates their application to concrete problems of independent interest. Numerous examples and proofs are provided. Working from basic definitions through to current research areas, this book can be used as a guide for graduate students interested in this field, or as a helpful survey for experts. Background needed for a potential reader of the book consists of a working knowledge of real and complex analysis on the level of first- and second-year graduate courses.

Chapel Hill Ergodic Theory Workshops

Author : Idris Assani
Publisher : American Mathematical Soc.
ISBN 13 : 0821833138
Total Pages : 184 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Chapel Hill Ergodic Theory Workshops by : Idris Assani

Download or read book Chapel Hill Ergodic Theory Workshops written by Idris Assani and published by American Mathematical Soc.. This book was released on 2004 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew out of two ergodic theory workshops held at the University of North Carolina at Chapel Hill. These events gave young researchers an introduction to active research areas and promoted interaction between young and established mathematicians. Included are research and survey articles devoted to various topics in ergodic theory. The book is suitable for graduate students and researchers interested in these and related areas.

Mathematics of Complexity and Dynamical Systems

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
ISBN 13 : 1461418054
Total Pages : 1885 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Mathematics of Complexity and Dynamical Systems by : Robert A. Meyers

Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

From Fourier Analysis and Number Theory to Radon Transforms and Geometry

Author : Hershel M. Farkas
Publisher : Springer Science & Business Media
ISBN 13 : 1461440742
Total Pages : 567 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis From Fourier Analysis and Number Theory to Radon Transforms and Geometry by : Hershel M. Farkas

Download or read book From Fourier Analysis and Number Theory to Radon Transforms and Geometry written by Hershel M. Farkas and published by Springer Science & Business Media. This book was released on 2012-09-18 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: A memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis’s contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore.A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.

Operator Theoretic Aspects of Ergodic Theory

Author : Tanja Eisner
Publisher : Springer
ISBN 13 : 3319168983
Total Pages : 630 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Operator Theoretic Aspects of Ergodic Theory by : Tanja Eisner

Download or read book Operator Theoretic Aspects of Ergodic Theory written by Tanja Eisner and published by Springer. This book was released on 2015-11-18 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include: • an intuitive introduction to ergodic theory • an introduction to the basic notions, constructions, and standard examples of topological dynamical systems • Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem • measure-preserving dynamical systems • von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem • strongly and weakly mixing systems • an examination of notions of isomorphism for measure-preserving systems • Markov operators, and the related concept of a factor of a measure preserving system • compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition • an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence Principle, theorems of Roth and Furstenberg–Sárközy) Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory

Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem

Author : Anatole Katok
Publisher : Cambridge University Press
ISBN 13 : 1139496867
Total Pages : 320 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem by : Anatole Katok

Download or read book Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem written by Anatole Katok and published by Cambridge University Press. This book was released on 2011-06-16 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems.

Borel Equivalence Relations

Author : Vladimir Grigorʹevich Kanoveĭ
Publisher : American Mathematical Soc.
ISBN 13 : 0821844539
Total Pages : 254 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Borel Equivalence Relations by : Vladimir Grigorʹevich Kanoveĭ

Download or read book Borel Equivalence Relations written by Vladimir Grigorʹevich Kanoveĭ and published by American Mathematical Soc.. This book was released on 2008 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Over the last 20 years, the theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. The book presents, for the first time in mathematical literature, all major aspects of this theory and its applications."--BOOK JACKET.

Inevitable Randomness in Discrete Mathematics

Author : Jzsef Beck
Publisher : American Mathematical Soc.
ISBN 13 : 0821847562
Total Pages : 267 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Inevitable Randomness in Discrete Mathematics by : Jzsef Beck

Download or read book Inevitable Randomness in Discrete Mathematics written by Jzsef Beck and published by American Mathematical Soc.. This book was released on 2009-09-01 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics has been called the science of order. The subject is remarkably good for generalizing specific cases to create abstract theories. However, mathematics has little to say when faced with highly complex systems, where disorder reigns. This disorder can be found in pure mathematical arenas, such as the distribution of primes, the $3n+1$ conjecture, and class field theory. The purpose of this book is to provide examples--and rigorous proofs--of the complexity law: (1) discrete systems are either simple or they exhibit advanced pseudorandomness; (2) a priori probabilities often exist even when there is no intrinsic symmetry. Part of the difficulty in achieving this purpose is in trying to clarify these vague statements. The examples turn out to be fascinating instances of deep or mysterious results in number theory and combinatorics. This book considers randomness and complexity. The traditional approach to complexity--computational complexity theory--is to study very general complexity classes, such as P, NP and PSPACE. What Beck does is very different: he studies interesting concrete systems, which can give new insights into the mystery of complexity. The book is divided into three parts. Part A is mostly an essay on the big picture. Part B is partly new results and partly a survey of real game theory. Part C contains new results about graph games, supporting the main conjecture. To make it accessible to a wide audience, the book is mostly self-contained.

Computational Geometry of Positive Definite Quadratic Forms

Author : Achill Schurmann
Publisher : American Mathematical Soc.
ISBN 13 : 082184735X
Total Pages : 183 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Computational Geometry of Positive Definite Quadratic Forms by : Achill Schurmann

Download or read book Computational Geometry of Positive Definite Quadratic Forms written by Achill Schurmann and published by American Mathematical Soc.. This book was released on 2009 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Starting from classical arithmetical questions on quadratic forms, this book takes the reader step by step through the connections with lattice sphere packing and covering problems. As a model for polyhedral reduction theories of positive definite quadratic forms, Minkowski's classical theory is presented, including an application to multidimensional continued fraction expansions. The reduction theories of Voronoi are described in great detail, including full proofs, new views, and generalizations that cannot be found elsewhere. Based on Voronoi's second reduction theory, the local analysis of sphere coverings and several of its applications are presented. These include the classification of totally real thin number fields, connections to the Minkowski conjecture, and the discovery of new, sometimes surprising, properties of exceptional structures such as the Leech lattice or the root lattices." "Throughout this book, special attention is paid to algorithms and computability, allowing computer-assisted treatments. Although dealing with relatively classical topics that have been worked on extensively by numerous authors, this book is exemplary in showing how computers may help to gain new insights."--BOOK JACKET.

Residues and Duality for Projective Algebraic Varieties

Author : Ernst Kunz
Publisher : American Mathematical Soc.
ISBN 13 : 0821847600
Total Pages : 177 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Residues and Duality for Projective Algebraic Varieties by : Ernst Kunz

Download or read book Residues and Duality for Projective Algebraic Varieties written by Ernst Kunz and published by American Mathematical Soc.. This book was released on 2008 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of (possibly singular) algebraic varieties over algebraically closed base fields. It describes duality and residue theorems in terms of Kahler differential forms and their residues. The properties of residues are introduced via local cohomology. Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations." "The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership, D. A. Cox explains toric residues and relates them to the earlier text." "The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given."--BOOK JACKET.