Aspects of Ergodic, Qualitative and Statistical Theory of Motion, Giovanni Gallavotti; Federico Bonetto; Guido Genti

Название: Ergodic theory.
ISBN: 3319498452 ISBN-13(EAN): 9783319498454
Издательство: Springer
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Описание: This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. The more advanced material includes Popa`s cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy. The structure of the book is designed to be flexible enough to serve a variety of readers.

Автор: Furstenberg Harry
Название: Recurrence in Ergodic Theory and Combinatorial Number Theory
ISBN: 0691615365 ISBN-13(EAN): 9780691615363
Издательство: Wiley
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Описание: Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make

Автор: Ricardo Mane; Silvio Levy
Название: Ergodic Theory and Differentiable Dynamics
ISBN: 3642703372 ISBN-13(EAN): 9783642703379
Издательство: Springer
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Описание: Rio de Janeiro, January 1987 Ricardo Mane Introduction This book is an introduction to ergodic theory, with emphasis on its relationship with the theory of differentiable dynamical systems, which is sometimes called differentiable ergodic theory.

Автор: Robert Edward Bowen; David Ruelle; Jean-Ren? Chazo
Название: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms
ISBN: 3540776052 ISBN-13(EAN): 9783540776055
Издательство: Springer
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Описание: Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen`s monograph immediately became a classic.

Автор: Jean Moulin Ollagnier
Название: Ergodic Theory and Statistical Mechanics
ISBN: 3540151923 ISBN-13(EAN): 9783540151920
Издательство: Springer
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Автор: Walters, Peter
Название: An Introduction to Ergodic Theory
ISBN: 0387951520 ISBN-13(EAN): 9780387951522
Издательство: Springer
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Описание: The first part of this introduction to ergodic theory addresses measure-preserving transformations of probability spaces and covers such topics as recurrence properties and the Birkhoff ergodic theorem. The second part focuses on the ergodic theory of continuous transformations of compact metrizable spaces.

Автор: Tanja Eisner; B?lint Farkas; Markus Haase; Rainer
Название: Operator Theoretic Aspects of Ergodic Theory
ISBN: 3319371053 ISBN-13(EAN): 9783319371054
Издательство: Springer
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Описание: What is Ergodic Theory?.- Topological Dynamical Systems.- Minimality and Recurrence.- The C*-algebra C(K) and the Koopman Operator.- Measure-Preserving Systems.- Recurrence and Ergodicity.- The Banach Lattice Lp and the Koopman Operator.- The Mean Ergodic Theorem.- Mixing Dynamical Systems.- Mean Ergodic Operators on C(K).- The Pointwise Ergodic Theorem.- Isomorphisms and Topological Models.- Markov Operators.- Compact Semigroups and Groups.- Topological Dynamics Revisited.- The Jacobs-de Leeuw-Glicksberg Decomposition.- Dynamical Systems with Discrete Spectrum.- A Glimpse at Arithmetic Progressions.- Joinings.- The Host-Kra-​Tao Theorem.- More Ergodic Theorems.- Appendix A: Topology.- Appendix B: Measure and Integration Theory.- Appendix C: Functional Analysis.- Appendix D: The Riesz Representation Theorem.- Appendix E: Theorems of Eberlein, Grothendieck, and Ellis.

Автор: Eisner Tanja
Название: Operator Theoretic Aspects of Ergodic Theory
ISBN: 3319168975 ISBN-13(EAN): 9783319168975
Издательство: Springer
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Описание: Stunning recent results by Host-Kra, Green-Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory.
Topics include:
- an intuitive introduction to ergodic theory
- an introduction to the basic notions, constructions, and standard examples of topological dynamical systems
- Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand-Naimark theorem
- measure-preserving dynamical systems
- von Neumann's Mean Ergodic Theorem and Birkhoff's Pointwise Ergodic Theorem
- strongly and weakly mixing systems
- an examination of notions of isomorphism for measure-preserving systems
- Markov operators, and the related concept of a factor of a measure preserving system
- compact groups and semigroups, and a powerful tool in their study, the Jacobs-de Leeuw-Glicksberg decomposition
- an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai, and Hindman, Furstenberg's Correspondence Principle, theorems of Roth and Furstenberg-S rk zy)
Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory

Автор: Yury A. Kutoyants
Название: Statistical Inference for Ergodic Diffusion Processes
ISBN: 184996906X ISBN-13(EAN): 9781849969062
Издательство: Springer
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Описание: The first book in inference for stochastic processes from a statistical, rather than a probabilistic, perspective. It provides a systematic exposition of theoretical results from over ten years of mathematical literature and presents, for the first time in book form, many new techniques and approaches.

Автор: Wael Bahsoun; Christopher Bose; Gary Froyland
Название: Ergodic Theory, Open Dynamics, and Coherent Structures
ISBN: 149394326X ISBN-13(EAN): 9781493943265
Издательство: Springer
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Описание: This book is comprised of selected research articles developed from a workshop on Ergodic Theory, Probabilistic Methods and Applications, held in April 2012 at the Banff International Research Station.

Автор: L. Sucheston
Название: Contributions to Ergodic Theory and Probability
ISBN: 3540051880 ISBN-13(EAN): 9783540051886
Издательство: Springer
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