Book Description
These lecture notes provide a unique introduction to Pesin theory and its applications.
Author : Mark Pollicott
Publisher : Cambridge University Press
Page : 176 pages
File Size : 20,21 MB
Release : 1993-02-04
Category : Mathematics
ISBN : 9780521435932
These lecture notes provide a unique introduction to Pesin theory and its applications.
Author : Paul Richard Halmos
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 31,36 MB
Release : 1956
Category : Ergodic theory
ISBN :
This classic book is based on lectures given by the author at the University of Chicago in 1956. The topics covered include, in particular, recurrence, the ergodic theorems, and a general discussion of ergodicity and mixing properties. There is also a general discussion of the relation between conjugacy and equivalence. With minimal prerequisites of some analysis and measure theory, this work can be used for a one-semester course in ergodic theory or for self-study.
Author : Luis Barreira
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 37,56 MB
Release : 2013-05-30
Category : Mathematics
ISBN : 0821898531
This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapun
Author : Karl E. Petersen
Publisher : Cambridge University Press
Page : 343 pages
File Size : 18,34 MB
Release : 1989-11-23
Category : Mathematics
ISBN : 1316583201
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 : M. Denker
Publisher : Lecture Notes in Mathematics
Page : 372 pages
File Size : 35,75 MB
Release : 1976-07
Category : Mathematics
ISBN :
Author : Karma Dajani
Publisher : CRC Press
Page : 268 pages
File Size : 18,33 MB
Release : 2021-07-04
Category : Mathematics
ISBN : 1000402770
A First Course in Ergodic Theory provides readers with an introductory course in Ergodic Theory. This textbook has been developed from the authors’ own notes on the subject, which they have been teaching since the 1990s. Over the years they have added topics, theorems, examples and explanations from various sources. The result is a book that is easy to teach from and easy to learn from — designed to require only minimal prerequisites. Features Suitable for readers with only a basic knowledge of measure theory, some topology and a very basic knowledge of functional analysis Perfect as the primary textbook for a course in Ergodic Theory Examples are described and are studied in detail when new properties are presented.
Author : Idris Assani
Publisher : Walter de Gruyter GmbH & Co KG
Page : 156 pages
File Size : 11,10 MB
Release : 2024-06-04
Category : Mathematics
ISBN : 3111435504
This book grew out of the 2021 Chapel Hill Ergodic Theory Workshop (https://ergwork.web.unc.edu/schedule-of-talks-201/) during which young and senior researchers presented recent advances in ergodic theory and dynamical systems. Included are original research and survey articles devoted to various topics in Ergodic Theory and Dynamical Systems. Some are from presenters at this workshop. This book attracts young and senior researchers alike.
Author : I. P. Cornfeld
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 23,58 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461569273
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 : I︠A︡kov Grigorʹevich Sinaĭ
Publisher : Princeton University Press
Page : 151 pages
File Size : 27,2 MB
Release : 1976
Category : Ergodic theory
ISBN : 0691081824
Author :
Publisher : Academic Press
Page : 201 pages
File Size : 38,51 MB
Release : 1976-11-15
Category : Mathematics
ISBN : 0080873863
Ergodic Theory and Topological Dynamics