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Foundations of Ergodic Theory
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  • Cited by 9
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    Lopes, Artur O 2018. A formula for the entropy of the convolution of Gibbs probabilities on the circle. Nonlinearity, Vol. 31, Issue. 7, p. 3441.

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  • Marcelo Viana, Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro , Krerley Oliveira, Universidade Federal de Alagoas, Brazil

Book description

Rich with examples and applications, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. The authors' clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their use of concrete examples illustrates these ideas and puts the results into perspective. The book requires few prerequisites, with background material supplied in the appendix. The first four chapters cover elementary material suitable for undergraduate students – invariance, recurrence and ergodicity – as well as some of the main examples. The authors then gradually build up to more sophisticated topics, including correlations, equivalent systems, entropy, the variational principle and thermodynamical formalism. The 400 exercises increase in difficulty through the text and test the reader's understanding of the whole theory. Hints and solutions are provided at the end of the book.


'The book provides the student or researcher with an excellent reference and/or base from which to move into current research in ergodic theory. This book would make an excellent text for a graduate course on ergodic theory.'

Douglas P. Dokken Source: Mathematical Reviews

'… Viana and Oliveira have written yet another excellent textbook! It may be fruitfully used to guide a graduate course in dynamical systems, or a topics seminar at either advanced undergraduate or early graduate levels. The book is designed so that the instructor may cull a variety of courses from its contents. The authors deserve special kudos for their collection of over 400 exercises, many with hints and solutions at the end of the book. As a further bonus, if only to pique the reader’s interest, a number of recent research results and open problems are sprinkled throughout the book.'

Tushar Das Source: MAA Reivews

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