Weakly Wandering Sequences In Ergodic Theory
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Weakly Wandering Sequences In Ergodic Theory
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Author : Stanley Eigen
language : en
Publisher: Springer
Release Date : 2014-08-19
Weakly Wandering Sequences In Ergodic Theory written by Stanley Eigen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-19 with Mathematics categories.
The appearance of weakly wandering (ww) sets and sequences for ergodic transformations over half a century ago was an unexpected and surprising event. In time it was shown that ww and related sequences reflected significant and deep properties of ergodic transformations that preserve an infinite measure. This monograph studies in a systematic way the role of ww and related sequences in the classification of ergodic transformations preserving an infinite measure. Connections of these sequences to additive number theory and tilings of the integers are also discussed. The material presented is self-contained and accessible to graduate students. A basic knowledge of measure theory is adequate for the reader.
Weakly Wandering Sequences In Ergodic Theory
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Author : Stanley Eigen
language : en
Publisher:
Release Date : 2014-09-30
Weakly Wandering Sequences In Ergodic Theory written by Stanley Eigen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-30 with categories.
Contributions To Ergodic Theory And Probability
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Author :
language : en
Publisher: Springer
Release Date : 2006-11-15
Contributions To Ergodic Theory And Probability written by and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
Invitation To Ergodic Theory
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Author : César Ernesto Silva
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Invitation To Ergodic Theory written by César Ernesto Silva 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 2008 with Mathematics categories.
"Several examples of a dynamical system are developed in detail to illustrate various dynamical concepts. These include in particular the baker's transformation, irrational rotations, the dyadic odometer, the Hajian-Kakutani transformation, the Gauss transformation, and the Chacon transformation. There is a detailed discussion of cutting and stacking transformations in ergodic theory. The book includes several exercises and some open questions to give the flavor of current research. The book also introduces some notions from topological dynamics, such as minimality, transitivity and symbolic spaces; and develops some metric topology, including the Baire category theorem."--BOOK JACKET.
Ergodic Theorems
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Author : Ulrich Krengel
language : en
Publisher: Walter de Gruyter
Release Date : 2011-03-01
Ergodic Theorems written by Ulrich Krengel and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-01 with Mathematics categories.
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
Studies In Probability And Ergodic Theory
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Author : Gian-Carlo Rota
language : en
Publisher:
Release Date : 1978
Studies In Probability And Ergodic Theory written by Gian-Carlo Rota and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Coupling methods for markov processes; On fluctuations of sums of random variables; Almost-sure invariance principle for branching brownian motion; On operator inequalities and projections; Boundary behavior of laplace-stieltjes transforms with applications to uniformly distributed sequences; Regularities of distribution; Strong liftings on topological measured spaces; Mixing transformations in an infinite measure space; On eventually weakly wandering sequences; Gap sequences and eventually weakly wandering sequences; The breakdown of automorphisms of compact topological groups; On the polynomial uniformity of translations on the n-torus; Generalized torus automorphisms are bernoullian; The isomorphism theorem for generalized Bernoulli Schemes; Measurabletransformations on homogeneous spaces; Ergodic transformations of lebesgue spaces.
Ergodic Theory
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Author : Karl E. Petersen
language : en
Publisher: Cambridge University Press
Release Date : 1989-11-23
Ergodic Theory written by Karl E. Petersen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-11-23 with Mathematics categories.
The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated.
Modern Dynamical Systems And Applications
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Author : Michael Brin
language : en
Publisher: Cambridge University Press
Release Date : 2004-08-16
Modern Dynamical Systems And Applications written by Michael Brin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-16 with Mathematics categories.
This volume presents a wide cross-section of current research in the theory of dynamical systems and contains articles by leading researchers, including several Fields medalists, in a variety of specialties. These are surveys, usually with new results included, as well as research papers that are included because of their potentially high impact. Major areas covered include hyperbolic dynamics, elliptic dynamics, mechanics, geometry, ergodic theory, group actions, rigidity, applications. The target audience includes dynamicists, who will find new results in their own specialty as well as surveys in others, and mathematicians from other disciplines wholook for a sample of current developments in ergodic theory and dynamical systems.
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