| Description |
1 online resource (xxi, 694 pages) : illustrations (some color) |
| Series |
Springer Nature reference |
|
Encyclopedia of complexity and systems science, 2629-2343 |
|
Springer Nature reference.
|
|
Encyclopedia of complexity and systems science series, 2629-2343
|
| Contents |
Introduction to Ergodic Theory -- Ergodic Theory: Basic Examples and Constructions -- Ergodicity and Mixing Properties -- Ergodic Theory: Recurrence -- Ergodic Theorems -- Spectral Theory of Dynamical Systems -- Joinings in Ergodic Theory -- Entropy in Ergodic Theory -- Isomorphism Theory in Ergodic Theory -- Dynamical Systems of Probabilistic Origin: Gaussian and Poisson Systems -- Ergodic Theory: Non-singular Transformations -- Sarnak's Conjecture from the Ergodic Theory Point of View -- Smooth Ergodic Theory -- Ergodic and spectral theory of area-preserving flows on surfaces -- Pressure and Equilibrium States in Ergodic Theory -- Parallels Between Topological Dynamics and Ergodic Theory -- Symbolic Dynamics -- Operator ergodic theory -- Dynamical Systems and C-algebras -- The complexity and the structure and classification of Dynamical Systems -- Ergodic Theory: Interactions with Combinatorics and Number Theory -- Ergodic Theory on Homogeneous Spaces and Metric Number Theory -- Ergodic Theory: Rigidity -- Chaos and Ergodic Theory -- Ergodic Theory: Fractal Geometry |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Description based on online resource; title from digital title page (viewed on September 01, 2023) |
| Subject |
Ergodic theory.
|
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Ergodic theory.
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| Form |
Electronic book
|
| Author |
Silva, César Ernesto, 1955- editor.
|
|
Danilenko, Alexandre I. editor
|
| ISBN |
9781071623886 |
|
1071623885 |
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