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Ergodic Theorems And Related Problems


Ergodic Theorems And Related Problems
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Ergodic Theorems And Related Problems


Ergodic Theorems And Related Problems
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Author : V. M. Shurenkov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-05

Ergodic Theorems And Related Problems written by V. M. Shurenkov 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 2018-11-05 with Mathematics categories.


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Ergodic Theorems For Group Actions


Ergodic Theorems For Group Actions
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Author : A.A. Tempelman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Ergodic Theorems For Group Actions written by A.A. Tempelman 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 2013-04-17 with Mathematics categories.


This volume is devoted to generalizations of the classical Birkhoff and von Neuman ergodic theorems to semigroup representations in Banach spaces, semigroup actions in measure spaces, homogeneous random fields and random measures on homogeneous spaces. The ergodicity, mixing and quasimixing of semigroup actions and homogeneous random fields are considered as well. In particular homogeneous spaces, on which all homogeneous random fields are quasimixing are introduced and studied (the n-dimensional Euclidean and Lobachevsky spaces with n>=2, and all simple Lie groups with finite centre are examples of such spaces. Also dealt with are applications of general ergodic theorems for the construction of specific informational and thermodynamical characteristics of homogeneous random fields on amenable groups and for proving general versions of the McMillan, Breiman and Lee-Yang theorems. A variational principle which characterizes the Gibbsian homogeneous random fields in terms of the specific free energy is also proved. The book has eight chapters, a number of appendices and a substantial list of references. For researchers whose works involves probability theory, ergodic theory, harmonic analysis, measure theory and statistical Physics.



Recurrence In Ergodic Theory And Combinatorial Number Theory


Recurrence In Ergodic Theory And Combinatorial Number Theory
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Author : Harry Furstenberg
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14

Recurrence In Ergodic Theory And Combinatorial Number Theory written by Harry Furstenberg and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.


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.



Ergodic Theory


Ergodic Theory
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Author : Manfred Einsiedler
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-11

Ergodic Theory written by Manfred Einsiedler 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 2010-09-11 with Mathematics categories.


This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.



Lectures On Ergodic Theory


Lectures On Ergodic Theory
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Author : Paul Richard Halmos
language : en
Publisher: American Mathematical Soc.
Release Date : 1956

Lectures On Ergodic Theory written by Paul Richard Halmos 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 1956 with Mathematics categories.


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.



Topics In Ergodic Theory


Topics In Ergodic Theory
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Author : William Parry
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-03

Topics In Ergodic Theory written by William Parry 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 2004-06-03 with Mathematics categories.


An introduction to topics and examples of ergodic theory, a central area of pure mathematics.



Ergodic Theory And Related Topics Iii


Ergodic Theory And Related Topics Iii
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Author : Ulrich Krengel
language : en
Publisher: Springer
Release Date : 2006-11-14

Ergodic Theory And Related Topics Iii written by Ulrich Krengel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.


The purpose of the conference was to represent recent developments in measure theoretic, differentiable and topological dynamical systems as well as connections to probability theory, stochastic processes, operator theory and statistical physics. Only original research papers that do not appear elsewhere are included in the proceedings. Their topics include: C(2)-diffeomorphisms of compact Riemann manifolds, geodesic flows, chaotic behaviour in billards, nonlinear ergodic theory, central limit theorems for subadditive processes, Hausdorff measures for parabolic rational maps, Markov operators, periods of cycles, Julia sets, ergodic theorems. From the Contents: L.A. Bunimovich: On absolutely focusing mirrors.- M. Denker, M. Urbanski: The dichotomy of Hausdorff measures and equilibrium states for parabolic rational maps.- F. Ledrappier: Ergodic properties of the stable foliations.- U. Wacker: Invariance principles and central limit theorems for nonadditive stationary processes.- J. Schmeling, R. Siegmund-Schultze: Hoelder continuity of the holonomy map for hyperbolic basic sets.- A.M. Blokh: The spectral decomposition, periods of cycles and Misiurewicz conjecture for graph maps.- and contributions by Chr. Bandt and K. Keller, T. Bogenschutz andH. Crauel, H.G. Bothe, M. Denker and K.F. Kramer, T.P. Hill and U. Krengel, A. Iwanik, Z.S. Kowalski, E. Lesigne, J. Malczak, I. Mizera, J. Sipos, R. Wittmann.



Wiener Wintner Ergodic Theorems


Wiener Wintner Ergodic Theorems
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Author : Idris Assani
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-05-22

Wiener Wintner Ergodic Theorems written by Idris Assani and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-22 with Mathematics categories.


The Wiener Wintner ergodic theorem is a strengthening of Birkhoff pointwise ergodic theorem. Announced by N Wiener and A Wintner, this theorem has introduced the study of a general phenomenon in ergodic theory in which samplings are “good” for an uncountable number of systems. We study the rate of convergence in the uniform version of this theorem and what we call Wiener Wintner dynamical systems and prove for these systems two pointwise results: the a.e. double recurrence theorem and the a.e. continuity of the fractional rotated ergodic Hilbert transform. Some extensions of the Wiener Wintner ergodic theorem are also given.



Ergodic Theory Of Random Transformations


Ergodic Theory Of Random Transformations
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Author : Yuri Kifer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Ergodic Theory Of Random Transformations written by Yuri Kifer 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 2012-12-06 with Mathematics categories.


Ergodic theory of dynamical systems i.e., the qualitative analysis of iterations of a single transformation is nowadays a well developed theory. In 1945 S. Ulam and J. von Neumann in their short note [44] suggested to study ergodic theorems for the more general situation when one applies in turn different transforma tions chosen at random. Their program was fulfilled by S. Kakutani [23] in 1951. 'Both papers considered the case of transformations with a common invariant measure. Recently Ohno [38] noticed that this condition was excessive. Ergodic theorems are just the beginning of ergodic theory. Among further major developments are the notions of entropy and characteristic exponents. The purpose of this book is the study of the variety of ergodic theoretical properties of evolution processes generated by independent applications of transformations chosen at random from a certain class according to some probability distribution. The book exhibits the first systematic treatment of ergodic theory of random transformations i.e., an analysis of composed actions of independent random maps. This set up allows a unified approach to many problems of dynamical systems, products of random matrices and stochastic flows generated by stochastic differential equations.



Fixed Point Theory And Applications Proceedings Of The Second International Conference


Fixed Point Theory And Applications Proceedings Of The Second International Conference
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Author : Kok Keong Tan
language : en
Publisher: World Scientific
Release Date : 1992-08-08

Fixed Point Theory And Applications Proceedings Of The Second International Conference written by Kok Keong Tan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-08 with categories.


This volume contains current works of researchers from twelve different countries on fixed point theory and applications. Topics include, in part, nonexpansive mappings, multifunctions, minimax inequalities, applications to game theory and computation of fixed points. It is valuable to pure and applied mathematicians as well as computing scientists and mathematical economists.