Positive Transfer Operators And Decay Of Correlations

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Positive Transfer Operators And Decay Of Correlations

Viviane Baladi
Positive Transfer Operators And Decay Of Correlations Book PDF

Author : Viviane Baladi
Publisher : World Scientific
Page : 326 pages
File Size : 50,5 Mb
Release : 2000-07-12
Category : Science
ISBN : 9789814496667

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Positive Transfer Operators And Decay Of Correlations by Viviane Baladi Pdf

Although individual orbits of chaotic dynamical systems are by definition unpredictable, the average behavior of typical trajectories can often be given a precise statistical description. Indeed, there often exist ergodic invariant measures with special additional features. For a given invariant measure, and a class of observables, the correlation functions tell whether (and how fast) the system “mixes”, i.e. “forgets” its initial conditions.This book, addressed to mathematicians and mathematical (or mathematically inclined) physicists, shows how the powerful technology of transfer operators, imported from statistical physics, has been used recently to construct relevant invariant measures, and to study the speed of decay of their correlation functions, for many chaotic systems. Links with dynamical zeta functions are explained.The book is intended for graduate students or researchers entering the field, and the technical prerequisites have been kept to a minimum.

Transfer Operators, Endomorphisms, and Measurable Partitions

Sergey Bezuglyi,Palle E. T. Jorgensen
Transfer Operators Endomorphisms and Measurable Partitions Book PDF

Author : Sergey Bezuglyi,Palle E. T. Jorgensen
Publisher : Springer
Page : 162 pages
File Size : 45,6 Mb
Release : 2018-06-21
Category : Mathematics
ISBN : 9783319924175

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Transfer Operators, Endomorphisms, and Measurable Partitions by Sergey Bezuglyi,Palle E. T. Jorgensen Pdf

The subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an emphasis on irreversible systems, the text presents a framework of multi-resolutions tailored for the study of endomorphisms, beginning with a systematic look at the latter. This entails a whole new set of tools, often quite different from those used for the “easier” and well-documented case of automorphisms. Among them is the construction of a family of positive operators (transfer operators), arising naturally as a dual picture to that of endomorphisms. The setting (close to one initiated by S. Karlin in the context of stochastic processes) is motivated by a number of recent applications, including wavelets, multi-resolution analyses, dissipative dynamical systems, and quantum theory. The automorphism-endomorphism relationship has parallels in operator theory, where the distinction is between unitary operators in Hilbert space and more general classes of operators such as contractions. There is also a non-commutative version: While the study of automorphisms of von Neumann algebras dates back to von Neumann, the systematic study of their endomorphisms is more recent; together with the results in the main text, the book includes a review of recent related research papers, some by the co-authors and their collaborators.

Smooth Ergodic Theory and Its Applications

A. B. Katok
Smooth Ergodic Theory and Its Applications Book PDF

Author : A. B. Katok
Publisher : American Mathematical Soc.
Page : 895 pages
File Size : 44,5 Mb
Release : 2001
Category : Ergodic theory
ISBN : 9780821826829

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Smooth Ergodic Theory and Its Applications by A. B. Katok Pdf

During the past decade, there have been several major new developments in smooth ergodic theory, which have attracted substantial interest to the field from mathematicians as well as scientists using dynamics in their work. In spite of the impressive literature, it has been extremely difficult for a student-or even an established mathematician who is not an expert in the area-to acquire a working knowledge of smooth ergodic theory and to learn how to use its tools. Accordingly, the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications (Seattle, WA) had a strong educational component, including ten mini-courses on various aspects of the topic that were presented by leading experts in the field. This volume presents the proceedings of that conference. Smooth ergodic theory studies the statistical properties of differentiable dynamical systems, whose origin traces back to the seminal works of Poincare and later, many great mathematicians who made contributions to the development of the theory. The main topic of this volume, smooth ergodic theory, especially the theory of nonuniformly hyperbolic systems, provides the principle paradigm for the rigorous study of complicated or chaotic behavior in deterministic systems. This paradigm asserts that if a non-linear dynamical system exhibits sufficiently pronounced exponential behavior, then global properties of the system can be deduced from studying the linearized system. One can then obtain detailed information on topological properties (such as the growth of periodic orbits, topological entropy, and dimension of invariant sets including attractors), as well as statistical properties (such as the existence of invariant measures, asymptotic behavior of typical orbits, ergodicity, mixing, decay of corre This volume serves a two-fold purpose: first, it gives a useful gateway to smooth ergodic theory for students and nonspecialists, and second, it provides a state-of-the-art report on important current aspects of the subject. The book is divided into three parts: lecture notes consisting of three long expositions with proofs aimed to serve as a comprehensive and self-contained introduction to a particular area of smooth ergodic theory; thematic sections based on mini-courses or surveys held at the conference; and original contributions presented at the meeting or closely related to the topics that were discussed there.

Modeling, Dynamics, Optimization and Bioeconomics I

Alberto Adrego Pinto,David Zilberman
Modeling Dynamics Optimization and Bioeconomics I Book PDF

Author : Alberto Adrego Pinto,David Zilberman
Publisher : Springer
Page : 753 pages
File Size : 52,7 Mb
Release : 2014-06-20
Category : Mathematics
ISBN : 9783319048499

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Modeling, Dynamics, Optimization and Bioeconomics I by Alberto Adrego Pinto,David Zilberman Pdf

This volume explores the emerging and current, cutting-edge theories and methods of modeling, optimization, dynamics and bio economy. It provides an overview of the main issues, results and open questions in these fields as well as covers applications to biology, economy, energy, industry, physics, psychology and finance. The majority of the contributed papers for this volume come from the participants of the International Conference on Modeling, Optimization and Dynamics (ICMOD 2010), a satellite conference of EURO XXIV Lisbon 2010, which took place at Faculty of Sciences of University of Porto, Portugal and from the Berkeley Bio economy Conference 2012, at the University of California, Berkeley, USA.

Contributions of Mexican Mathematicians Abroad in Pure and Applied Mathematics

Juan Carlos Pardo Millán,Pedro Solórzano
Contributions of Mexican Mathematicians Abroad in Pure and Applied Mathematics Book PDF

Author : Juan Carlos Pardo Millán,Pedro Solórzano
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 41,9 Mb
Release : 2018
Category : Mathematicians
ISBN : 9781470442866

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Contributions of Mexican Mathematicians Abroad in Pure and Applied Mathematics by Juan Carlos Pardo Millán,Pedro Solórzano Pdf

This volume contains the proceedings of the Second Workshop of Mexican Mathematicians Abroad (II Reunión de Matemáticos Mexicanos en el Mundo), held from December 15–19, 2014, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. This meeting was the second in a series of ongoing biannual meetings aimed at showcasing the research of Mexican mathematicians based outside of Mexico. The book features articles drawn from eight broad research areas: algebra, analysis, applied mathematics, combinatorics, dynamical systems, geometry, probability theory, and topology. Their topics range from novel applications of non-commutative probability to graph theory, to interactions between dynamical systems and geophysical flows. Several articles survey the fields and problems on which the authors work, highlighting research lines currently underrepresented in Mexico. The research-oriented articles provide either alternative approaches to well-known problems or new advances in active research fields. The wide selection of topics makes the book accessible to advanced graduate students and researchers in mathematics from different fields.

Geometry and Analysis of Fractals

De-Jun Feng,Ka-Sing Lau
Geometry and Analysis of Fractals Book PDF

Author : De-Jun Feng,Ka-Sing Lau
Publisher : Springer
Page : 360 pages
File Size : 49,8 Mb
Release : 2014-08-01
Category : Mathematics
ISBN : 9783662439203

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Geometry and Analysis of Fractals by De-Jun Feng,Ka-Sing Lau Pdf

This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.

Ergodic Theory, Open Dynamics, and Coherent Structures

Wael Bahsoun,Christopher Bose,Gary Froyland
Ergodic Theory Open Dynamics and Coherent Structures Book PDF

Author : Wael Bahsoun,Christopher Bose,Gary Froyland
Publisher : Springer Science & Business
Page : 240 pages
File Size : 48,5 Mb
Release : 2014-05-02
Category : Mathematics
ISBN : 9781493904198

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Ergodic Theory, Open Dynamics, and Coherent Structures by Wael Bahsoun,Christopher Bose,Gary Froyland Pdf

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. It contains contributions from world leading experts in ergodic theory, numerical dynamical systems, molecular dynamics and ocean/atmosphere dynamics, nonequilibrium statistical mechanics. The volume will serve as a valuable reference for mathematicians, physicists, engineers, biologists and climate scientists, who currently use, or wish to learn how to use, probabilistic techniques to cope with dynamical models that display open or non-equilibrium behavior.

Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot

Michel Laurent Lapidus,Machiel Van Frankenhuysen
Fractal Geometry and Applications A Jubilee of Benoit Mandelbrot Book PDF

Author : Michel Laurent Lapidus,Machiel Van Frankenhuysen
Publisher : American Mathematical Soc.
Page : 760 pages
File Size : 54,9 Mb
Release : 2004
Category : Mathematics
ISBN : 0821836374

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Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot by Michel Laurent Lapidus,Machiel Van Frankenhuysen Pdf

This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.

Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology

Jens Bölte,Frank Steiner
Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology Book PDF

Author : Jens Bölte,Frank Steiner
Publisher : Cambridge University Press
Page : 285 pages
File Size : 52,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9781107610491

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Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology by Jens Bölte,Frank Steiner Pdf

Leading experts introduce this classical subject with exciting new applications in theoretical physics.

European Congress of Mathematics

Carles Casacuberta,Rosa Maria Miro-Roig,Joan Verdera,Sebastia Xambo-Descamps
European Congress of Mathematics Book PDF

Author : Carles Casacuberta,Rosa Maria Miro-Roig,Joan Verdera,Sebastia Xambo-Descamps
Publisher : Birkhäuser
Page : 611 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882682

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European Congress of Mathematics by Carles Casacuberta,Rosa Maria Miro-Roig,Joan Verdera,Sebastia Xambo-Descamps Pdf

This is the first volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: R. Ahlswede, V. Bach, V. Baladi, J. Bruna, N. Burq, X. Cabré, P.J. Cameron, Z. Chatzidakis, C. Ciliberto, G. Dal Maso, J. Denef, R. Dijkgraaf, B. Fantechi, H. Föllmer, A.B. Goncharov, A. Grigor'yan, M. Harris, R. Iturriaga, K. Johansson, K. Khanin, P. Koskela, H.W. Lenstra, Jr., F. Loeser, Y.I. Manin, N.S. Manton, Y. Meyer, I. Moerdijk, E.M. Opdam, T. Peternell, B.M.A.G. Piette, A. Reznikov, H. Schlichtkrull, B. Schmidt, K. Schmidt, C. Simó, B. Tóth, E. van den Ban, M.-F. Vignéras, O. Viro.

Second Summer School in Analysis and Mathematical Physics

m Summer School in Analysis and Mathematical Physics 2000 Cuernavaca,Salvador Pérez-Esteva,Carlos Villegas-Blas,Summer School in Analysis and Mathematical Physics
Second Summer School in Analysis and Mathematical Physics Book PDF

Author : m Summer School in Analysis and Mathematical Physics 2000 Cuernavaca,Salvador Pérez-Esteva,Carlos Villegas-Blas,Summer School in Analysis and Mathematical Physics
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 54,6 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821827086

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Second Summer School in Analysis and Mathematical Physics by m Summer School in Analysis and Mathematical Physics 2000 Cuernavaca,Salvador Pérez-Esteva,Carlos Villegas-Blas,Summer School in Analysis and Mathematical Physics Pdf

For the second time, a Summer School in Analysis and Mathematical Physics took place at the Universidad Nacional Autonoma de Mexico in Cuernavaca. The purpose of the schools is to provide a bridge from standard graduate courses in mathematics to current research topics, particularly in analysis. The lectures are given by internationally recognized specialists in the fields. The topics covered in this Second Summer School include harmonic analysis, complex analysis, pseudodifferential operators, the mathematics of quantum chaos, and non-linear analysis.

Statistical Properties of Deterministic Systems

Jiu Ding,Aihui Zhou
Statistical Properties of Deterministic Systems Book PDF

Author : Jiu Ding,Aihui Zhou
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 43,7 Mb
Release : 2010-06-28
Category : Mathematics
ISBN : 9783540853671

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Statistical Properties of Deterministic Systems by Jiu Ding,Aihui Zhou Pdf

Part of Tsinghua University Texts, "Statistical Properties of Deterministic Systems" discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two problems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system. The book can be used as a text for graduate students in applied mathematics and in computational mathematics; it can also serve as a reference book for researchers in the physical sciences, life sciences, and engineering. Dr. Jiu Ding is a professor at the Department of Mathematics of the University of Southern Mississippi; Dr. Aihui Zhou is a professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences.

Asymptotic Methods in Stochastics

Lajos Horvath and Barbara Szyszkowicz
Asymptotic Methods in Stochastics Book PDF

Author : Lajos Horvath and Barbara Szyszkowicz
Publisher : American Mathematical Soc.
Page : 552 pages
File Size : 48,7 Mb
Release : 2024-06-28
Category : Asymptotic expansions
ISBN : 082187148X

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Asymptotic Methods in Stochastics by Lajos Horvath and Barbara Szyszkowicz Pdf

Honoring over forty years of Miklos Csorgo's work in probability and statistics, this title shows the state of the research. This book covers such topics as: path properties of stochastic processes, weak convergence of random size sums, almost sure stability of weighted maxima, and procedures for detecting changes in statistical models.

Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps

Viviane Baladi
Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps Book PDF

Author : Viviane Baladi
Publisher : Springer
Page : 291 pages
File Size : 54,9 Mb
Release : 2018-05-09
Category : Mathematics
ISBN : 9783319776613

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Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps by Viviane Baladi Pdf

The spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators. In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endomorphisms, showing how the (isotropic) function spaces relevant there can be studied via Paley–Littlewood decompositions, and allowing easier access to the construction of the anisotropic spaces which is performed in the second part. This is the first book describing the use of anisotropic spaces in dynamics. Aimed at researchers and graduate students, it presents results and techniques developed since the beginning of the twenty-first century.

Thermodynamic Formalism

David Ruelle
Thermodynamic Formalism Book PDF

Author : David Ruelle
Publisher : Cambridge University Press
Page : 198 pages
File Size : 51,5 Mb
Release : 2004-11-25
Category : Science
ISBN : 1139455281

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Thermodynamic Formalism by David Ruelle Pdf

Reissued in the Cambridge Mathematical Library this classic book outlines the theory of thermodynamic formalism which was developed to describe the properties of certain physical systems consisting of a large number of subunits. It is aimed at mathematicians interested in ergodic theory, topological dynamics, constructive quantum field theory, the study of certain differentiable dynamical systems, notably Anosov diffeomorphisms and flows. It is also of interest to theoretical physicists concerned with the conceptual basis of equilibrium statistical mechanics. The level of the presentation is generally advanced, the objective being to provide an efficient research tool and a text for use in graduate teaching. Background material on mathematics has been collected in appendices to help the reader. Extra material is given in the form of updates of problems that were open at the original time of writing and as a new preface specially written for this new edition by the author.