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Classical And Dynamical Markov And Lagrange Spectra Dynamical Fractal And Arithmetic Aspects
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Book Synopsis Classical and Dynamical Markov and Lagrange Spectra by : Davi Lima
Download or read book Classical and Dynamical Markov and Lagrange Spectra written by Davi Lima and published by . This book was released on 2020-09-14 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book intends to give a modern presentation of the classical Markov and Lagrange spectrum, which are fundamental objects from the theory of Diophantine approximations and of their several generalizations related to Dynamical Systems and Differential Geometry. Besides presenting many classical results, the book includes several topics of recent research on the subject, connecting several fields of Mathematics -- Number Theory, Dynamical Systems and Fractal Geometry. It includes topics as: Classical results on the Markov and Lagrange spectra: the Markov theorem on the lower spectra The fractal geometry of the complement of the Lagrange spectrum in the Markov spectrum Continuity of Hausdorff dimension of the spectra intersected with half-lines: the classical spectra and dynamical generalizations Intervals in the classical spectra and dynamical generalizations The beginning of the spectra: discrete initial part and first accumulation points (in the classical and dynamical cases) Markov and Lagrange spectra for Teichmüller dynamics
Book Synopsis Classical And Dynamical Markov And Lagrange Spectra : Dynamical, Fractal and Arithmetic Aspects by : Davi Lima
Download or read book Classical And Dynamical Markov And Lagrange Spectra : Dynamical, Fractal and Arithmetic Aspects written by Davi Lima and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classical And Dynamical Markov And Lagrange Spectra: Dynamical, Fractal And Arithmetic Aspects by : Davi Dos Santos Lima
Download or read book Classical And Dynamical Markov And Lagrange Spectra: Dynamical, Fractal And Arithmetic Aspects written by Davi Dos Santos Lima and published by World Scientific. This book was released on 2020-09-18 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book intends to give a modern presentation of the classical Markov and Lagrange spectrum, which are fundamental objects from the theory of Diophantine approximations and of their several generalizations related to Dynamical Systems and Differential Geometry. Besides presenting many classical results, the book includes several topics of recent research on the subject, connecting several fields of Mathematics — Number Theory, Dynamical Systems and Fractal Geometry.It includes topics as:
Book Synopsis Topological and Ergodic Theory of Symbolic Dynamics by : Henk Bruin
Download or read book Topological and Ergodic Theory of Symbolic Dynamics written by Henk Bruin and published by American Mathematical Society. This book was released on 2022-12-21 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.
Book Synopsis The Markoff and Lagrange Spectra by : Thomas W. Cusick
Download or read book The Markoff and Lagrange Spectra written by Thomas W. Cusick and published by American Mathematical Soc.. This book was released on 1989 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is directed at mathematicians interested in Diophantine approximation and the theory of quadratic forms and the relationship of these subjects to Markoff and Lagrange spectra. The authors have gathered and systemized numerous results from the diverse and scattered literature, much of which has appeared in rather inaccessible Russian publications. Readers will find a comprehensive overview of the theory of the Markoff and Lagrange spectra, starting with the origins of the subject in two papers of A. Markoff from 1879-80. Most of the progress since that time has occurred in the last 20 years or so, when there has been a resurgence of interest in these spectra. The authors provide an excellent exposition of these developments, in addition to presenting many proofs and correcting various errors in the literature.
Download or read book Physics Briefs written by and published by . This book was released on 1993 with total page 1288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Complex Analysis and Dynamical Systems by : Mark Agranovsky
Download or read book Complex Analysis and Dynamical Systems written by Mark Agranovsky and published by Birkhäuser. This book was released on 2018-01-31 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.
Book Synopsis Chaos Theory Tamed by : Garnett Williams
Download or read book Chaos Theory Tamed written by Garnett Williams and published by CRC Press. This book was released on 1997-09-09 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents.
Book Synopsis Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations by : Jacob Palis Júnior
Download or read book Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations written by Jacob Palis Júnior and published by Cambridge University Press. This book was released on 1995-01-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the classical theory and its generalizations, aimed at mathematicians and scientists working in dynamical systems.
Book Synopsis Introduction to the Modern Theory of Dynamical Systems by : Anatole Katok
Download or read book Introduction to the Modern Theory of Dynamical Systems written by Anatole Katok and published by Cambridge University Press. This book was released on 1995 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.
Book Synopsis Number Theory and Dynamical Systems by : M. M. Dodson
Download or read book Number Theory and Dynamical Systems written by M. M. Dodson and published by Cambridge University Press. This book was released on 1989-11-09 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987. There are close and surprising connections between number theory and dynamical systems. One emerged last century from the study of the stability of the solar system where problems of small divisors associated with the near resonance of planetary frequencies arose. Previously the question of the stability of the solar system was answered in more general terms by the celebrated KAM theorem, in which the relationship between near resonance (and so Diophantine approximation) and stability is of central importance. Other examples of the connections involve the work of Szemeredi and Furstenberg, and Sprindzuk. As well as containing results on the relationship between number theory and dynamical systems, the book also includes some more speculative and exploratory work which should stimulate interest in different approaches to old problems.
Book Synopsis Structure and Dynamics of Confined Polymers by : John J. Kasianowicz
Download or read book Structure and Dynamics of Confined Polymers written by John J. Kasianowicz and published by Springer Science & Business Media. This book was released on 2002-07-31 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polymers are essential to biology because they can have enough stable degrees of freedom to store the molecular code of heredity and to express the sequences needed to manufacture new molecules. Through these they perform or control virtually every function in life. Although some biopolymers are created and spend their entire career in the relatively large free space inside cells or organelles, many biopolymers must migrate through a narrow passageway to get to their targeted destination. This suggests the questions: How does confining a polymer affect its behavior and function? What does that tell us about the interactions between the monomers that comprise the polymer and the molecules that confine it? Can we design and build devices that mimic the functions of these nanoscale systems? The NATO Advanced Research Workshop brought together for four days in Bikal, Hungary over forty experts in experimental and theoretical biophysics, molecular biology, biophysical chemistry, and biochemistry interested in these questions. Their papers collected in this book provide insight on biological processes involving confinement and form a basis for new biotechnological applications using polymers. In his paper Edmund DiMarzio asks: What is so special about polymers? Why are polymers so prevalent in living things? The chemist says the reason is that a protein made of N amino acids can have any of 20 different kinds at each position along the chain, resulting in 20 N different polymers, and that the complexity of life lies in this variety.
Download or read book Chemical Abstracts written by and published by . This book was released on with total page 2762 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Modeling by : Mark M. Meerschaert
Download or read book Mathematical Modeling written by Mark M. Meerschaert and published by Elsevier. This book was released on 2007-06-18 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modeling, Third Edition is a general introduction to an increasingly crucial topic for today's mathematicians. Unlike textbooks focused on one kind of mathematical model, this book covers the broad spectrum of modeling problems, from optimization to dynamical systems to stochastic processes. Mathematical modeling is the link between mathematics and the rest of the world. Meerschaert shows how to refine a question, phrasing it in precise mathematical terms. Then he encourages students to reverse the process, translating the mathematical solution back into a comprehensible, useful answer to the original question. This textbook mirrors the process professionals must follow in solving complex problems. Each chapter in this book is followed by a set of challenging exercises. These exercises require significant effort on the part of the student, as well as a certain amount of creativity. Meerschaert did not invent the problems in this book--they are real problems, not designed to illustrate the use of any particular mathematical technique. Meerschaert's emphasis on principles and general techniques offers students the mathematical background they need to model problems in a wide range of disciplines. Increased support for instructors, including MATLAB material New sections on time series analysis and diffusion models Additional problems with international focus such as whale and dolphin populations, plus updated optimization problems
Book Synopsis Hyperbolic Chaos by : Sergey P. Kuznetsov
Download or read book Hyperbolic Chaos written by Sergey P. Kuznetsov and published by Springer Science & Business Media. This book was released on 2012-03-20 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
Book Synopsis Non-Newtonian Calculus by : Michael Grossman
Download or read book Non-Newtonian Calculus written by Michael Grossman and published by Non-Newtonian Calculus. This book was released on 1972 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The non-Newtonian calculi provide a wide variety of mathematical tools for use in science, engineering, and mathematics. They appear to have considerable potential for use as alternatives to the classical calculus of Newton and Leibniz. It may well be that these calculi can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.
Book Synopsis Statistical Mechanics by : James Sethna
Download or read book Statistical Mechanics written by James Sethna and published by OUP Oxford. This book was released on 2006-04-07 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.
