Weakly Wandering Sequences in Ergodic Theory PDF Download
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Author: Stanley Eigen
Publisher: Springer
ISBN: 4431551085
Category : Mathematics
Languages : en
Pages : 164
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Book Description
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.
Author: Stanley Eigen
Publisher: Springer
ISBN: 4431551085
Category : Mathematics
Languages : en
Pages : 164
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Book Description
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.
Author:
Publisher: Springer
ISBN: 3540363718
Category : Mathematics
Languages : en
Pages : 291
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Book Description
Author: Jon Aaronson
Publisher: American Mathematical Soc.
ISBN: 0821804944
Category : Mathematics
Languages : en
Pages : 298
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Book Description
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.
Author: César Ernesto Silva
Publisher: American Mathematical Soc.
ISBN: 0821844202
Category : Mathematics
Languages : en
Pages : 274
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Book Description
"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.
Author: Gian-Carlo Rota
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 352
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Book Description
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.
Author: Karl E. Petersen
Publisher: Cambridge University Press
ISBN: 9780521389976
Category : Mathematics
Languages : en
Pages : 348
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Book Description
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.
Author: Michael Brin
Publisher: Cambridge University Press
ISBN: 9780521840736
Category : Mathematics
Languages : en
Pages : 490
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Book Description
This volume presents a broad collection of current research by leading experts in the theory of dynamical systems.
Author: Cesar E. Silva
Publisher: Springer Nature
ISBN: 1071623885
Category : Mathematics
Languages : en
Pages : 707
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Book Description
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: Ulrich Krengel
Publisher: Walter de Gruyter
ISBN: 3110844648
Category : Mathematics
Languages : en
Pages : 369
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Book Description
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.
Author: James C. Alexander
Publisher: Springer
ISBN: 3540459464
Category : Mathematics
Languages : en
Pages : 736
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Book Description
The papers in this volume reflect the richness and diversity of the subject of dynamics. Some are lectures given at the three conferences (Ergodic Theory and Topological Dynamics, Symbolic Dynamics and Coding Theory and Smooth Dynamics, Dynamics and Applied Dynamics) held in Maryland between October 1986 and March 1987; some are work which was in progress during the Special Year, and some are work which was done because of questions and problems raised at the conferences. In addition, a paper of John Milnor and William Thurston, versions of which had been available as notes but not yet published, is included.
