Entropy in Dynamical Systems

by Downarowicz, Tomasz

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A comprehensive course on entropy in dynamical systems ideal for graduate students learning the subject from scratch.

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Title Statements

Full title :Entropy in Dynamical Systems.

Summary

A comprehensive course on entropy in dynamical systems ideal for graduate students learning the subject from scratch.

Edition Statements

Publication Date:2011.

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge
Language:eng
Publication Date:2011.

Notes

7.5 Tail entropy and asymptotic h-expansiveness in dimension zero.

The Physical Object

Description:1 online resource (406 pages)

Edition Identifiers

ISBN:9781139187985, 1139187988, 9780511976155, 0511976151, 9780521888851, 0521888859, 9781139190589, 113919058X, 9781139185677, 1139185675, 1107219310, 9781107219311, 1283383926, 9781283383929, 9786613383921, 6613383929, 1139183362, 9781139183369
oclc:ocn782877021
LC Classification:QA611.5 .D685 2011
Dewey Decimal:515.39

Cover; Entropy in Dynamical Systems; NEW MATHEMATICAL MONOGRAPHS; Title; Copyright; To my Parents; Contents; Preface; Acknowledgments; Introduction; 0.1 The leitmotiv; 0.2 A few words about the history of entropy; 0.3 Multiple meanings of entropy; 0.3.1 Entropy in physics; 0.3.2 Shannon entropy; 0.3.3 Connection between Shannon and Boltzmann entropy; 0.3.4 Dynamical entropy; 0.3.5 Dynamical entropy as data compression rate; 0.3.6 Entropy as disorder; 0.4 Conventions; Part I Entropy in ergodic theory; 1 Shannon information and entropy; 1.1 Information and entropy of probability vectors.

1.2 Partitions and sigma-algebras1.3 Information and static entropy of a partition; 1.4 Conditional static entropy; 1.5 Conditional entropy via probabilistic tools*; 1.6 Basic properties of static entropy; 1.7 Metrics on the space of partitions; 1.8 Mutual information*; 1.9 Non-Shannon inequalities*; Exercises; 2 Dynamical entropy of a process; 2.1 Subadditivity; 2.2 Preliminaries on dynamical systems; 2.3 Dynamical entropy of a process; 2.4 Properties of dynamical entropy; 2.5 Affinity of dynamical entropy; 2.6 Conditional dynamical entropy via disintegration*

2.7 Summary of the properties of ent…

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