Ergodic Theory And Dynamical Systems In Their Interactions With Arithmetics And Combinatorics

Author : Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Publisher : Springer
Page : 434 pages
File Size : 52,5 Mb
Release : 2018-06-15
Category : Mathematics
ISBN : 9783319749082

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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk Pdf

This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.

Author : N. Pytheas Fogg
Publisher : Springer
Page : 404 pages
File Size : 52,7 Mb
Release : 2003-10-24
Category : Mathematics
ISBN : 9783540457145

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Substitutions in Dynamics, Arithmetics and Combinatorics by N. Pytheas Fogg Pdf

A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.

Author : Henk Bruin
Publisher : American Mathematical Society
Page : 481 pages
File Size : 49,9 Mb
Release : 2023-01-20
Category : Mathematics
ISBN : 9781470469849

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Topological and Ergodic Theory of Symbolic Dynamics by Henk Bruin Pdf

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.

Author : Idris Assani
Publisher : Walter de Gruyter GmbH & Co KG
Page : 148 pages
File Size : 48,9 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9783110460919

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Ergodic Theory by Idris Assani Pdf

This monograph discusses recent advances in ergodic theory and dynamical systems. As a mixture of survey papers of active research areas and original research papers, this volume attracts young and senior researchers alike. Contents: Duality of the almost periodic and proximal relations Limit directions of a vector cocycle, remarks and examples Optimal norm approximation in ergodic theory The iterated Prisoner’s Dilemma: good strategies and their dynamics Lyapunov exponents for conservative twisting dynamics: a survey Takens’ embedding theorem with a continuous observable

Author : Harry Furstenberg
Publisher : Princeton University Press
Page : 216 pages
File Size : 44,8 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400855162

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Recurrence in Ergodic Theory and Combinatorial Number Theory by Harry Furstenberg Pdf

Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. 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.

Author : Cesar E. Silva,Alexandre I. Danilenko
Publisher : Springer Nature
Page : 707 pages
File Size : 53,7 Mb
Release : 2023-07-31
Category : Mathematics
ISBN : 9781071623886

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Ergodic Theory by Cesar E. Silva,Alexandre I. Danilenko Pdf

This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras

Author : Bryna Kra,Robert A. Meyers
Publisher : Springer
Page : 320 pages
File Size : 40,5 Mb
Release : 2011-04
Category : Mathematics
ISBN : 1441993517

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Ergodic Theory and Applications by Bryna Kra,Robert A. Meyers Pdf

Ergodic theory lies at the intersection of numerous areas of mathematics. This volume includes authoritative entries from the Encyclopedia of Complexity and Systems Science and covers basic topics in addition to ones in related fields.

Author : Mark Pollicott,Michiko Yuri
Publisher : Cambridge University Press
Page : 198 pages
File Size : 42,8 Mb
Release : 1998-01-29
Category : Mathematics
ISBN : 0521575990

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Dynamical Systems and Ergodic Theory by Mark Pollicott,Michiko Yuri Pdf

This book is an essentially self contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a masters level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der waerden's theorem and szemerdi's theorem).

Author : Sidney A. Morris
Publisher : MDPI
Page : 160 pages
File Size : 50,9 Mb
Release : 2019-03-05
Category : Mathematics
ISBN : 9783038976448

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Topological Groups by Sidney A. Morris Pdf

Following the tremendous reception of our first volume on topological groups called "Topological Groups: Yesterday, Today, and Tomorrow", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Well-known researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.

Author : Mahmoud Filali
Publisher : Walter de Gruyter GmbH & Co KG
Page : 307 pages
File Size : 49,6 Mb
Release : 2020-08-24
Category : Mathematics
ISBN : 9783110600438

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Banach Algebras and Applications by Mahmoud Filali Pdf

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Author : Karma Dajani,Cor Kraaikamp
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 51,6 Mb
Release : 2002-12-31
Category : Mathematics
ISBN : 9780883850343

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Ergodic Theory of Numbers by Karma Dajani,Cor Kraaikamp Pdf

Ergodic Theory of Numbers looks at the interaction between two fields of mathematics: number theory and ergodic theory (as part of dynamical systems). It is an introduction to the ergodic theory behind common number expansions, like decimal expansions, continued fractions, and many others. However, its aim does not stop there. For undergraduate students with sufficient background knowledge in real analysis and graduate students interested in the area, it is also an introduction to a "dynamical way of thinking". The questions studied here are dynamical as well as number theoretical in nature, and the answers are obtained with the help of ergodic theory. Attention is focused on concepts like measure-preserving, ergodicity, natural extension, induced transformations, and entropy. These concepts are then applied to familiar expansions to obtain old and new results in an elegant and straightforward manner. What it means to be ergodic and the basic ideas behind ergodic theory will be explained along the way. The subjects covered vary from classical to recent, which makes this book appealing to researchers as well as students.

Author : Anatoly M. Vershik,Victor M. Buchstaber,Andrey V. Malyutin
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 49,7 Mb
Release : 2021-08-30
Category : Education
ISBN : 9781470456641

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Topology, Geometry, and Dynamics: V. A. Rokhlin-Memorial by Anatoly M. Vershik,Victor M. Buchstaber,Andrey V. Malyutin Pdf

Vladimir Abramovich Rokhlin (8/23/1919–12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory. The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-100, held from August 19–23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia. The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.

Author : I. P. Cornfeld,S. V. Fomin,Y. G. Sinai
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461569275

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Ergodic Theory by I. P. Cornfeld,S. V. Fomin,Y. G. Sinai Pdf

Ergodic theory is one of the few branches of mathematics which has changed radically during the last two decades. Before this period, with a small number of exceptions, ergodic theory dealt primarily with averaging problems and general qualitative questions, while now it is a powerful amalgam of methods used for the analysis of statistical properties of dyna mical systems. For this reason, the problems of ergodic theory now interest not only the mathematician, but also the research worker in physics, biology, chemistry, etc. The outline of this book became clear to us nearly ten years ago but, for various reasons, its writing demanded a long period of time. The main principle, which we adhered to from the beginning, was to develop the approaches and methods or ergodic theory in the study of numerous concrete examples. Because of this, Part I of the book contains the description of various classes of dynamical systems, and their elementary analysis on the basis of the fundamental notions of ergodicity, mixing, and spectra of dynamical systems. Here, as in many other cases, the adjective" elementary" i~ not synonymous with "simple. " Part II is devoted to "abstract ergodic theory. " It includes the construc tion of direct and skew products of dynamical systems, the Rohlin-Halmos lemma, and the theory of special representations of dynamical systems with continuous time. A considerable part deals with entropy.

Author : A. B. Katok
Publisher : Unknown
Page : 333 pages
File Size : 55,8 Mb
Release : 1981
Category : Differentiable dynamical systems
ISBN : 3764330368

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Ergodic Theory and Dynamical Systems by A. B. Katok Pdf

Author : Jan de Gier,Cheryl E. Praeger,Terence Tao
Publisher : Springer Nature
Page : 803 pages
File Size : 41,7 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9783030624972

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2019-20 MATRIX Annals by Jan de Gier,Cheryl E. Praeger,Terence Tao Pdf

MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.