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There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. This text presents a series of essays on the topic.
Tutorial survey papers on important areas of ergodic theory, with related research papers.
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.
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
This book concerns areas of ergodic theory that are now being intensively developed. The topics include entropy theory (with emphasis on dynamical systems with multi-dimensional time), elements of the renormalization group method in the theory of dynamical systems, splitting of separatrices, and some problems related to the theory of hyperbolic dynamical systems. Originally published in 1993. 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.
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
This book grew out of the 2021 Chapel Hill Ergodic Theory Workshop (https://ergwork.web.unc.edu/schedule-of-talks-201/) during which young and senior researchers presented recent advances in ergodic theory and dynamical systems. Included are original research and survey articles devoted to various topics in Ergodic Theory and Dynamical Systems. Some are from presenters at this workshop. This book attracts young and senior researchers alike.
Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.
Ergodic theory is a field that is stimulating on its own, and also in its interactions with other branches of mathematics and science. In recent years, the interchanges with harmonic analysis have been especially noticeable and productive. This book contains survey papers describing the relationship of ergodic theory with convergence, rigidity theory and the theory of joinings. These papers present the background of each area of interaction, the most outstanding results and promising lines of research. They should form perfect starting points for anyone beginning research in one of these areas. Thirteen related research papers describe the work; several treat questions arising from the Furstenberg multiple recurrence theory, while the remainder deal with convergence and a variety of other topics in dynamics.