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![]( "Buchcover ISBN 9781071623879")
“Together the articles give a useful overview of the key ideas in ergodic theory across a great diversity of settings. As a reference to precise formulations of a huge array of concepts and methods in ergodic theory together with extensive specialised bibliographies in each article, this collection will undoubtedly be useful to researchers and postgraduate students in any field that has reason to call on these ideas.” (Thomas B. Ward, zbMATH 1532.37003, 2024)
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
