Combinatorial Constructions In Ergodic Theory And Dynamics
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Combinatorial Constructions In Ergodic Theory And Dynamics
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Author : A. B. Katok
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Combinatorial Constructions In Ergodic Theory And Dynamics written by A. B. Katok and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Ergodic theory studies measure-preserving transformations of measure spaces. These objects are intrinsically infinite, and the notion of an individual point or of an orbit makes no sense. Still there are a variety of situations when a measure preserving transformation (and its asymptotic behavior) can be well described as a limit of certain finite objects (periodic processes). The first part of this book develops this idea systematically. Genericity of approximation in various categories is explored, and numerous applications are presented, including spectral multiplicity and properties of the maximal spectral type. The second part of the book contains a treatment of various constructions of cohomological nature with an emphasis on obtaining interesting asymptotic behavior from approximate pictures at different time scales. The book presents a view of ergodic theory not found in other expository sources. It is suitable for graduate students familiar with measure theory and basic functional analysis.
Combinatorial Constructions In Ergodic Theory And Dynamics
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Author : A. B. Katok
language : en
Publisher:
Release Date : 2003
Combinatorial Constructions In Ergodic Theory And Dynamics written by A. B. Katok and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
Combinatorial Dynamics And Entropy In Dimension One
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Author : Alseda Luis
language : en
Publisher: World Scientific Publishing Company
Release Date : 1993-06-04
Combinatorial Dynamics And Entropy In Dimension One written by Alseda Luis and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06-04 with Mathematics categories.
In last thirty years an explosion of interest in the study of nonlinear dynamical systems occured. The theory of one-dimensional dynamical systems has grown out in many directions. One of them has its roots in the Sharkovski0 Theorem. This beautiful theorem describes the possible sets of periods of all cycles of maps of an interval into itself. Another direction has its main objective in measuring the complexity of a system, or the amount of chaos present in it. A good way of doing this is to compute topological entropy of the system. The aim of this book is to provide graduate students and researchers with a unified and detailed exposition of these developments for interval and circle maps. Many comments are added referring to related problems, and historical remarks are made. Request Inspection Copy
Combinatorial Constructions In Smooth Ergodic Theory
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Author : Philipp Kunde
language : en
Publisher:
Release Date : 2014
Combinatorial Constructions In Smooth Ergodic Theory written by Philipp Kunde and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Recurrence In Ergodic Theory And Combinatorial Number Theory
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Author : Harry Furstenberg
language : en
Publisher:
Release Date : 2016-04-19
Recurrence In Ergodic Theory And Combinatorial Number Theory written by Harry Furstenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Combinatorial number theory categories.
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 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.
Operator Theoretic Aspects Of Ergodic Theory
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Author : Tanja Eisner
language : en
Publisher: Springer
Release Date : 2015-11-18
Operator Theoretic Aspects Of Ergodic Theory written by Tanja Eisner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-18 with Mathematics categories.
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–Sárközy) 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
Dynamics Ergodic Theory And Geometry
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Author : Boris Hasselblatt
language : en
Publisher: Cambridge University Press
Release Date : 2007-09-24
Dynamics Ergodic Theory And Geometry written by Boris Hasselblatt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-24 with Mathematics categories.
Based on the subjects from the Clay Mathematics Institute/Mathematical Sciences Research Institute Workshop titled 'Recent Progress in Dynamics' in September and October 2004, this volume contains surveys and research articles by leading experts in several areas of dynamical systems that have experienced substantial progress. One of the major surveys is on symplectic geometry, which is closely related to classical mechanics and an exciting addition to modern geometry. The survey on local rigidity of group actions gives a broad and up-to-date account of another flourishing subject. Other papers cover hyperbolic, parabolic, and symbolic dynamics as well as ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this book fascinating. The book also includes a fifty-page commented problem list that takes the reader beyond the areas covered by the surveys, to inspire and guide further research.
Dynamical Systems And Ergodic Theory
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Author : Mark Pollicott
language : en
Publisher: Cambridge University Press
Release Date : 1998-01-29
Dynamical Systems And Ergodic Theory written by Mark Pollicott and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-29 with Mathematics categories.
This book is an essentially self contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a masters level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der waerden's theorem and szemerdi's theorem).
Ergodic Theory
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Author : Cesar E. Silva
language : en
Publisher: Springer Nature
Release Date : 2023-07-31
Ergodic Theory written by Cesar E. Silva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.
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
Combinatorial Dynamics And Entropy In Dimension One
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Author : Ll Alsedà
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2000
Combinatorial Dynamics And Entropy In Dimension One written by Ll Alsedà and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book introduces the reader to two of the main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all periodic orbits of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.: it is called combinatorial dynamics. The second direction has its main objective in measuring the complexity of a system, or the degree of "chaos" present in it. A good way of doing this is to study the topological entropy of the system. The aim of this book is to provide graduate students and researchers with a unified and detailed exposition of these developments for interval and circle maps. The second edition contains two new appendices, where an extension of the theory to tree and graph maps is presented without technical proofs.