Dimension Theory

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Publisher : Springer Nature
ISBN 13 : 3030222322
Total Pages : 262 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Dimension Theory by : Michael G. Charalambous

Download or read book Dimension Theory written by Michael G. Charalambous and published by Springer Nature. This book was released on 2019-10-08 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions. Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.

Dimension Theory in Dynamical Systems

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Publisher : University of Chicago Press
ISBN 13 : 0226662233
Total Pages : 633 pages
Book Rating : 4.2/5 (266 download)

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Book Synopsis Dimension Theory in Dynamical Systems by : Yakov B. Pesin

Download or read book Dimension Theory in Dynamical Systems written by Yakov B. Pesin and published by University of Chicago Press. This book was released on 2008-04-15 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principles of symmetry and self-similarity structure nature's most beautiful creations. For example, they are expressed in fractals, famous for their beautiful but complicated geometric structure, which is the subject of study in dimension theory. And in dynamics the presence of invariant fractals often results in unstable "turbulent-like" motions and is associated with "chaotic" behavior. In this book, Yakov Pesin introduces a new area of research that has recently appeared in the interface between dimension theory and the theory of dynamical systems. Focusing on invariant fractals and their influence on stochastic properties of systems, Pesin provides a comprehensive and systematic treatment of modern dimension theory in dynamical systems, summarizes the current state of research, and describes the most important accomplishments of this field. Pesin's synthesis of these subjects of broad current research interest will be appreciated both by advanced mathematicians and by a wide range of scientists who depend upon mathematical modeling of dynamical processes.

Dimension Theory

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Publisher : Academic Press
ISBN 13 : 0080873502
Total Pages : 271 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Dimension Theory by :

Download or read book Dimension Theory written by and published by Academic Press. This book was released on 1970-05-31 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dimension Theory

General Topology I

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Publisher : Springer Science & Business Media
ISBN 13 : 3642612652
Total Pages : 210 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis General Topology I by : A.V. Arkhangel'skii

Download or read book General Topology I written by A.V. Arkhangel'skii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of the encyclopaedia volumes devoted to general topology. It has two parts. The first outlines the basic concepts and constructions of general topology, including several topics which have not previously been covered in English language texts. The second part presents a survey of dimension theory, from the very beginnings to the most important recent developments. The principal ideas and methods are treated in detail, and the main results are provided with sketches of proofs. The authors have suceeded admirably in the difficult task of writing a book which will not only be accessible to the general scientist and the undergraduate, but will also appeal to the professional mathematician. The authors' efforts to detail the relationship between more specialized topics and the central themes of topology give the book a broad scholarly appeal which far transcends narrow disciplinary lines.

Dimension Theory (PMS-4), Volume 4

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Publisher : Princeton University Press
ISBN 13 : 1400875668
Total Pages : 174 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Dimension Theory (PMS-4), Volume 4 by : Witold Hurewicz

Download or read book Dimension Theory (PMS-4), Volume 4 written by Witold Hurewicz and published by Princeton University Press. This book was released on 2015-12-08 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book 4 in the Princeton Mathematical Series. Originally published in 1941. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Thermodynamic Formalism and Applications to Dimension Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 3034802064
Total Pages : 300 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Thermodynamic Formalism and Applications to Dimension Theory by : Luis Barreira

Download or read book Thermodynamic Formalism and Applications to Dimension Theory written by Luis Barreira and published by Springer Science & Business Media. This book was released on 2011-08-24 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems. In particular, the book considers three different flavors of the thermodynamic formalism, namely nonadditive, subadditive, and almost additive, and provides a detailed discussion of some of the most significant results in the area, some of them quite recent. It also includes a discussion of the most substantial applications of these flavors of the thermodynamic formalism to dimension theory and multifractal analysis of dynamical systems.

Modern Dimension Theory

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Publisher : Elsevier
ISBN 13 : 1483275027
Total Pages : 268 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Modern Dimension Theory by : Jun-Iti Nagata

Download or read book Modern Dimension Theory written by Jun-Iti Nagata and published by Elsevier. This book was released on 2014-05-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bibliotheca Mathematica, Volume 6: Modern Dimension Theory provides a brief account of dimension theory as it has been developed since 1941, including the principal results of the classical theory for separable metric spaces. This book discusses the decomposition theorem, Baire's zero-dimensional spaces, dimension of separable metric spaces, and characterization of dimension by a sequence of coverings. The imbedding of countable-dimensional spaces, sum theorem for strong inductive dimension, and cohomology group of a topological space are also elaborated. This text likewise covers the uniformly zero-dimensional mappings, theorems in euclidean space, transfinite inductive dimension, and dimension of non-metrizable spaces. This volume is recommended to students and specialists researching on dimension theory.

Dimension Theory of Hyperbolic Flows

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Publisher : Springer Science & Business Media
ISBN 13 : 3319005480
Total Pages : 155 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Dimension Theory of Hyperbolic Flows by : Luís Barreira

Download or read book Dimension Theory of Hyperbolic Flows written by Luís Barreira and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dimension theory of dynamical systems has progressively developed, especially over the last two decades, into an independent and extremely active field of research. Its main aim is to study the complexity of sets and measures that are invariant under the dynamics. In particular, it is essential to characterizing chaotic strange attractors. To date, some parts of the theory have either only been outlined, because they can be reduced to the case of maps, or are too technical for a wider audience. In this respect, the present monograph is intended to provide a comprehensive guide. Moreover, the text is self-contained and with the exception of some basic results in Chapters 3 and 4, all the results in the book include detailed proofs. The book is intended for researchers and graduate students specializing in dynamical systems who wish to have a sufficiently comprehensive view of the theory together with a working knowledge of its main techniques. The discussion of some open problems is also included in the hope that it may lead to further developments. Ideally, readers should have some familiarity with the basic notions and results of ergodic theory and hyperbolic dynamics at the level of an introductory course in the area, though the initial chapters also review all the necessary material.

Ergodic Theory, Hyperbolic Dynamics and Dimension Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 3642280900
Total Pages : 295 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Ergodic Theory, Hyperbolic Dynamics and Dimension Theory by : Luís Barreira

Download or read book Ergodic Theory, Hyperbolic Dynamics and Dimension Theory written by Luís Barreira and published by Springer Science & Business Media. This book was released on 2012-04-28 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.

Fractals and Universal Spaces in Dimension Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 0387854940
Total Pages : 259 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Fractals and Universal Spaces in Dimension Theory by : Stephen Lipscomb

Download or read book Fractals and Universal Spaces in Dimension Theory written by Stephen Lipscomb and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classical (separable metric) and the modern (not-necessarily separable metric). The classical theory is now well documented in several books. This monograph is the first book to unify the modern theory from 1960-2007. Like the classical theory, the modern theory fundamentally involves the unit interval. Unique features include: * The use of graphics to illustrate the fractal view of these spaces; * Lucid coverage of a range of topics including point-set topology and mapping theory, fractal geometry, and algebraic topology; * A final chapter contains surveys and provides historical context for related research that includes other imbedding theorems, graph theory, and closed imbeddings; * Each chapter contains a comment section that provides historical context with references that serve as a bridge to the literature. This monograph will be useful to topologists, to mathematicians working in fractal geometry, and to historians of mathematics. Being the first monograph to focus on the connection between generalized fractals and universal spaces in dimension theory, it will be a natural text for graduate seminars or self-study - the interested reader will find many relevant open problems which will create further research into these topics.

The Complete Dimension Theory of Partially Ordered Systems with Equivalence and Orthogonality

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Publisher : American Mathematical Soc.
ISBN 13 : 0821837168
Total Pages : 134 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Complete Dimension Theory of Partially Ordered Systems with Equivalence and Orthogonality by : K. R. Goodearl

Download or read book The Complete Dimension Theory of Partially Ordered Systems with Equivalence and Orthogonality written by K. R. Goodearl and published by American Mathematical Soc.. This book was released on 2005 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction Partial commutative monoids Continuous dimension scales Espaliers Classes of espaliers Bibliography Index

Conformal Dimension

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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.

Hyperspace

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Publisher : Oxford University Press
ISBN 13 : 0199857768
Total Pages : 377 pages
Book Rating : 4.1/5 (998 download)

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Book Synopsis Hyperspace by : Michio Kaku

Download or read book Hyperspace written by Michio Kaku and published by Oxford University Press. This book was released on 1994-03-24 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Are there other dimensions beyond our own? Is time travel possible? Can we change the past? Are there gateways to parallel universes? All of us have pondered such questions, but there was a time when scientists dismissed these notions as outlandish speculations. Not any more. Today, they are the focus of the most intense scientific activity in recent memory. In Hyperspace, Michio Kaku, author of the widely acclaimed Beyond Einstein and a leading theoretical physicist, offers the first book-length tour of the most exciting (and perhaps most bizarre) work in modern physics, work which includes research on the tenth dimension, time warps, black holes, and multiple universes. The theory of hyperspace (or higher dimensional space)--and its newest wrinkle, superstring theory--stand at the center of this revolution, with adherents in every major research laboratory in the world, including several Nobel laureates. Beginning where Hawking's Brief History of Time left off, Kaku paints a vivid portrayal of the breakthroughs now rocking the physics establishment. Why all the excitement? As the author points out, for over half a century, scientists have puzzled over why the basic forces of the cosmos--gravity, electromagnetism, and the strong and weak nuclear forces--require markedly different mathematical descriptions. But if we see these forces as vibrations in a higher dimensional space, their field equations suddenly fit together like pieces in a jigsaw puzzle, perfectly snug, in an elegant, astonishingly simple form. This may thus be our leading candidate for the Theory of Everything. If so, it would be the crowning achievement of 2,000 years of scientific investigation into matter and its forces. Already, the theory has inspired several thousand research papers, and has been the focus of over 200 international conferences. Michio Kaku is one of the leading pioneers in superstring theory and has been at the forefront of this revolution in modern physics. With Hyperspace, he has produced a book for general readers which conveys the vitality of the field and the excitement as scientists grapple with the meaning of space and time. It is an exhilarating look at physics today and an eye-opening glimpse into the ultimate nature of the universe.

Attractor Dimension Estimates for Dynamical Systems: Theory and Computation

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Publisher : Springer Nature
ISBN 13 : 3030509877
Total Pages : 555 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Attractor Dimension Estimates for Dynamical Systems: Theory and Computation by : Nikolay Kuznetsov

Download or read book Attractor Dimension Estimates for Dynamical Systems: Theory and Computation written by Nikolay Kuznetsov and published by Springer Nature. This book was released on 2020-07-02 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.

High-Dimensional Probability

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Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Collected Works of Witold Hurewicz

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Publisher : American Mathematical Soc.
ISBN 13 : 0821800116
Total Pages : 654 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Collected Works of Witold Hurewicz by : Witold Hurewicz

Download or read book Collected Works of Witold Hurewicz written by Witold Hurewicz and published by American Mathematical Soc.. This book was released on 1995 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers of the outstanding and versatile mathematician, Witold Hurewicz. Preceding the collection are introductory articles describing Hurewicz's contributions to Borel sets, dimension theory, and algebraic topology. Hurewicz first studied set theory and dimension, and his papers on this topic are especially clear and precise, making them accessible to beginning mathematicians. His work in algebraic topology is marked by five fundamental papers which provide an introduction to homotopy groups and the Hurewicz Theorem concerning the relation between homotopy and singular homology. These papers are included here in their original form along with English translations. Each paper in the collection is followed by a review from one of the major reviewing journals. These reviews were written by eminent mathematicians and serve as excellent abstracts for the papers.

Theory of Dimensions, Finite and Infinite

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Publisher :
ISBN 13 :
Total Pages : 424 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Theory of Dimensions, Finite and Infinite by : Ryszard Engelking

Download or read book Theory of Dimensions, Finite and Infinite written by Ryszard Engelking and published by . This book was released on 1995 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: