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The Ergodic Theory of Discrete Sample Paths

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Release : 1996
Genre : Mathematics
Kind : eBook
Book Rating : 774/5 ( reviews)

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Book Synopsis The Ergodic Theory of Discrete Sample Paths by : Paul C. Shields

Download or read book The Ergodic Theory of Discrete Sample Paths written by Paul C. Shields. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: This book is about finite-alphabet stationary processes, which are important in physics, engineering, and data compression. The focus is on the combinatorial properties of typical finite sample paths drawn from a stationary, ergodic process. A primary goal, only partially realized, is to develop a theory based directly on sample path arguments with minimal appeals to the probability formalism. A secondary goal is to give a careful presentation of the many models for stationary finite-alphabet processes that have been developed in probability theory, ergodic theory, and information theory.

The Ergodic Theory of Discrete Groups

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Release : 1989-08-17
Genre : Mathematics
Kind : eBook
Book Rating : 742/5 ( reviews)

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Book Synopsis The Ergodic Theory of Discrete Groups by : Peter J. Nicholls

Download or read book The Ergodic Theory of Discrete Groups written by Peter J. Nicholls. This book was released on 1989-08-17. Available in PDF, EPUB and Kindle. Book excerpt: The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. There has been a great resurgence of interest in the field, due in large measure to the pioneering work of Dennis Sullivan. Tools have been developed and applied with outstanding success to many deep problems. The ergodic theory of discrete groups has become a substantial field of mathematical research in its own right, and it is the aim of this book to provide a rigorous introduction from first principles to some of the major aspects of the theory. The particular focus of the book is on the remarkable measure supported on the limit set of a discrete group that was first developed by S. J. Patterson for Fuchsian groups, and later extended and refined by Sullivan.

Ergodic Theory

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Release : 2016-06-20
Genre : Mathematics
Kind : eBook
Book Rating : 912/5 ( reviews)

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Book Synopsis Ergodic Theory by : Idris Assani

Download or read book Ergodic Theory written by Idris Assani. This book was released on 2016-06-20. Available in PDF, EPUB and Kindle. Book excerpt: This monograph discusses recent advances in ergodic theory and dynamical systems. As a mixture of survey papers of active research areas and original research papers, this volume attracts young and senior researchers alike. Contents: Duality of the almost periodic and proximal relations Limit directions of a vector cocycle, remarks and examples Optimal norm approximation in ergodic theory The iterated Prisoner’s Dilemma: good strategies and their dynamics Lyapunov exponents for conservative twisting dynamics: a survey Takens’ embedding theorem with a continuous observable

Ergodic Theory

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Release : 2023-07-31
Genre : Mathematics
Kind : eBook
Book Rating : 885/5 ( reviews)

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Book Synopsis Ergodic Theory by : Cesar E. Silva

Download or read book Ergodic Theory written by Cesar E. Silva. This book was released on 2023-07-31. Available in PDF, EPUB and Kindle. Book excerpt: 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

Lectures on Ergodic Theory

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Release : 2017-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 848/5 ( reviews)

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Book Synopsis Lectures on Ergodic Theory by : Paul R. Halmos

Download or read book Lectures on Ergodic Theory written by Paul R. Halmos. This book was released on 2017-11-15. Available in PDF, EPUB and Kindle. Book excerpt: This concise classic by a well-known master of mathematical exposition covers recurrence, ergodic theorems, ergodicity and mixing properties, and the relation between conjugacy and equivalence. 1956 edition.

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