An Introduction To Infinite Ergodic Theory
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An Introduction To Infinite Ergodic Theory
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Author : Jon Aaronson
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
An Introduction To Infinite Ergodic Theory written by Jon Aaronson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations. The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behaviour, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible "ergodic behaviour" is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.
Ergodic Theory
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Author : Cesar E. Silva
language : en
Publisher: Springer Nature
Release Date : 2023-07-31
Ergodic Theory written by Cesar E. Silva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.
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
Infinite Ergodic Theory Of Numbers
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Author : Marc Kesseböhmer
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-10-10
Infinite Ergodic Theory Of Numbers written by Marc Kesseböhmer and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-10 with Mathematics categories.
By connecting dynamical systems and number theory, this graduate textbook on ergodic theory acts as an introduction to a highly active area of mathematics, where a variety of strands of research open up. The text explores various concepts in infinite ergodic theory, always using continued fractions and other number-theoretic dynamical systems as illustrative examples. Contents: Preface Mathematical symbols Number-theoretical dynamical systems Basic ergodic theory Renewal theory and α-sum-level sets Infinite ergodic theory Applications of infinite ergodic theory Bibliography Index
Ergodic Theory
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Author : Idris Assani
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-06-20
Ergodic Theory written by Idris Assani and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Mathematics categories.
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
Mathematics Of Complexity And Dynamical Systems
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Author : Robert A. Meyers
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-05
Mathematics Of Complexity And Dynamical Systems written by Robert A. Meyers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-05 with Mathematics categories.
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.
Combinatorial Constructions In Ergodic Theory And Dynamics
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Author : A. B. Katok
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Combinatorial Constructions In Ergodic Theory And Dynamics written by A. B. Katok and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
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.
Ergodic Theory
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Author : I. P. Cornfeld
language : en
Publisher: Springer
Release Date : 2012-07-02
Ergodic Theory written by I. P. Cornfeld and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-02 with Mathematics categories.
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.
Ergodic Theory Via Joinings
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Author : Eli Glasner
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Ergodic Theory Via Joinings written by Eli Glasner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This textbook focuses on the abstract aspects of topological dynamics and ergodic theory, and presents several examples of the joining technique. The author covers dynamical systems on Lebesgue spaces, the Koopman representation, isometric and weakly mixing extensions, the Furstenberg-Zimmer structure theorem, and the entropy theory for Z-systems. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com).
A Festschrift For Herman Rubin
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Author : Herman Rubin
language : en
Publisher: IMS
Release Date : 2004
A Festschrift For Herman Rubin written by Herman Rubin and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Knotted Surfaces And Their Diagrams
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Author : J. Scott Carter
language : en
Publisher: American Mathematical Society
Release Date : 2023-12-06
Knotted Surfaces And Their Diagrams written by J. Scott Carter and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-06 with Mathematics categories.
In this book the authors develop the theory of knotted surfaces in analogy with the classical case of knotted curves in 3-dimensional space. In the first chapter knotted surface diagrams are defined and exemplified; these are generic surfaces in 3-space with crossing information given. The diagrams are further enhanced to give alternative descriptions. A knotted surface can be described as a movie, as a kind of labeled planar graph, or as a sequence of words in which successive words are related by grammatical changes. In the second chapter, the theory of Reidemeister moves is developed in the various contexts. The authors show how to unknot intricate examples using these moves. The third chapter reviews the braid theory of knotted surfaces. Examples of the Alexander isotopy are given, and the braid movie moves are presented. In the fourth chapter, properties of the projections of knotted surfaces are studied. Oriented surfaces in 4-space are shown to have planar projections without cusps and without branch points. Signs of triple points are studied. Applications of triple-point smoothing that include proofs of triple-point formulas and a proof of Whitney's congruence on normal Euler classes are presented. The fifth chapter indicates how to obtain presentations for the fundamental group and the Alexander modules. Key examples are worked in detail. The Seifert algorithm for knotted surfaces is presented and exemplified. The sixth chapter relates knotted surfaces and diagrammatic techniques to 2-categories. Solutions to the Zamolodchikov equations that are diagrammatically obtained are presented. The book contains over 200 illustrations that illuminate the text. Examples are worked out in detail, and readers have the opportunity to learn first-hand a series of remarkable geometric techniques.