An Introduction To The Kolmogorov Bernoulli Equivalence
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An Introduction To The Kolmogorov Bernoulli Equivalence
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Author : Gabriel Ponce
language : en
Publisher: Springer Nature
Release Date : 2019-10-25
An Introduction To The Kolmogorov Bernoulli Equivalence written by Gabriel Ponce and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-25 with Mathematics categories.
This book offers an introduction to a classical problem in ergodic theory and smooth dynamics, namely, the Kolmogorov–Bernoulli (non)equivalence problem, and presents recent results in this field. Starting with a crash course on ergodic theory, it uses the class of ergodic automorphisms of the two tori as a toy model to explain the main ideas and technicalities arising in the aforementioned problem. The level of generality then increases step by step, extending the results to the class of uniformly hyperbolic diffeomorphisms, and concludes with a survey of more recent results in the area concerning, for example, the class of partially hyperbolic diffeomorphisms. It is hoped that with this type of presentation, nonspecialists and young researchers in dynamical systems may be encouraged to pursue problems in this area.
Thermodynamic Formalism
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Author : Mark Pollicott
language : en
Publisher: Springer Nature
Release Date : 2021-10-01
Thermodynamic Formalism written by Mark Pollicott and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-01 with Mathematics categories.
This volume arose from a semester at CIRM-Luminy on “Thermodynamic Formalism: Applications to Probability, Geometry and Fractals” which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area. Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry. This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.
Ergodic Theory And Differentiable Dynamics
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Author : Ricardo Mane
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ergodic Theory And Differentiable Dynamics written by Ricardo Mane and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a rich research field, there are always further topics that should arguably be included. Subjects like geodesic flows or the role of Hausdorff dimension in con temporary ergodic theory are two of the most tempting gaps to fill. However, I let it stand with practically the same boundaries as the original version, still believing these adequately fulfill its goal of presenting the basic knowledge required to approach the research area of Differentiable Ergodic Theory. I wish to thank Dr. Levy for the excellent translation and several of the correc tions mentioned above. 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. Chapter 0, a quick review of measure theory, is included as a reference. Proofs are omitted, except for some results on derivatives with respect to sequences of partitions, which are not generally found in standard texts on measure and integration theory and tend to be lost within a much wider framework in more advanced texts.
Dynamics Stochastics
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Author : Michael S. Keane
language : en
Publisher: IMS
Release Date : 2006
Dynamics Stochastics written by Michael S. Keane and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Restricted Orbit Equivalence For Actions Of Discrete Amenable Groups
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Author : Janet Whalen Kammeyer
language : en
Publisher: Cambridge University Press
Release Date : 2002-04-18
Restricted Orbit Equivalence For Actions Of Discrete Amenable Groups written by Janet Whalen Kammeyer 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 2002-04-18 with Computers categories.
This monograph offers a broad investigative tool in ergodic theory and measurable dynamics. The motivation for this work is that one may measure how similar two dynamical systems are by asking how much the time structure of orbits of one system must be distorted for it to become the other. Different restrictions on the allowed distortion will lead to different restricted orbit equivalence theories. These include Ornstein's Isomorphism theory, Kakutani Equivalence theory and a list of others. By putting such restrictions in an axiomatic framework, a general approach is developed that encompasses all of these examples simultaneously and gives insight into how to seek further applications.
Complexity Entropy And The Physics Of Information
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Author : Wojciech H. Zurek
language : en
Publisher: CRC Press
Release Date : 2018-03-08
Complexity Entropy And The Physics Of Information written by Wojciech H. Zurek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-08 with Science categories.
This book has emerged from a meeting held during the week of May 29 to June 2, 1989, at St. John’s College in Santa Fe under the auspices of the Santa Fe Institute. The (approximately 40) official participants as well as equally numerous “groupies” were enticed to Santa Fe by the above “manifesto.” The book—like the “Complexity, Entropy and the Physics of Information” meeting explores not only the connections between quantum and classical physics, information and its transfer, computation, and their significance for the formulation of physical theories, but it also considers the origins and evolution of the information-processing entities, their complexity, and the manner in which they analyze their perceptions to form models of the Universe. As a result, the contributions can be divided into distinct sections only with some difficulty. Indeed, I regard this degree of overlapping as a measure of the success of the meeting. It signifies consensus about the important questions and on the anticipated answers: they presumably lie somewhere in the “border territory,” where information, physics, complexity, quantum, and computation all meet.
Computer Science Theory And Applications
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Author : Dima Grigoriev
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-15
Computer Science Theory And Applications written by Dima Grigoriev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-15 with Computers categories.
The International Symposium on Computer Science in Russia (CSR 2006) was held on June 8–12, 2006 in St. Petersburg, Russia, hosted by the Steklov Institute of Mathematics at St. Petersburg.
An Introduction To Probability Theory
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Author : K. Itô
language : en
Publisher: Cambridge University Press
Release Date : 1984-09-28
An Introduction To Probability Theory written by K. Itô 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 1984-09-28 with Mathematics categories.
One of the most distinguished probability theorists in the world rigorously explains the basic probabilistic concepts while fostering an intuitive understanding of random phenomena.
The Logic Of Thermostatistical Physics
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Author : Gerard G. Emch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
The Logic Of Thermostatistical Physics written by Gerard G. Emch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
This book addresses several of the foundational problems in thermophysics, i. e. thermodynamics and statistical mechanics. It is an interdisciplinary work in that it examines the philosophical underpinning of scientific models and theories; it also refines the analysis of the problems at hand and delineates the place occupied by various scientific models in a generalized philosophical landscape. Hence, our philosophical - or theoretical - inquiry focuses sharply on the concept of models; and our empirical - or laboratory - evidence is sought in the model-building activities of scientists who have tried to confront the epistemological problems arising in the thermophysical sciences. Primarily for researchers and students in physics, philosophy of science, and mathematics, our book aims at informing the readers - with all the in dispensable technical details made readily available - about the nature of the foundational problems, how these problems are approached with the help of various mathematical models, and what the philosophical implications of such models and approaches involve. Some familiarity with elementary ther mophysics and/or with introductory-level philosophy of science may help, but neither is a prerequisite. The logical and mathematical background re quired for the book are introduced in the Appendices. Upon using the Subject Index, the readers may easily locate the concepts and theorems needed for understanding various parts of the book. The Citation Index lists the authors of the contributions we discuss in detail.
Stable And Random Motions In Dynamical Systems
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Author : Jurgen Moser
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Stable And Random Motions In Dynamical Systems written by Jurgen Moser and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Science categories.
For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.