Modern Theory Of Dynamical Systems A Tribute To Dmitry Victorovich Anosov

Author : Anatole Katok,Yakov Pesin,Federico Rodriguez Hertz
Publisher : American Mathematical Soc.
Page : 320 pages
File Size : 52,5 Mb
Release : 2017-06-19
Category : Boundary value problems
ISBN : 9781470425609

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Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov by Anatole Katok,Yakov Pesin,Federico Rodriguez Hertz Pdf

This volume is a tribute to one of the founders of modern theory of dynamical systems, the late Dmitry Victorovich Anosov. It contains both original papers and surveys, written by some distinguished experts in dynamics, which are related to important themes of Anosov's work, as well as broadly interpreted further crucial developments in the theory of dynamical systems that followed Anosov's original work. Also included is an article by A. Katok that presents Anosov's scientific biography and a picture of the early development of hyperbolicity theory in its various incarnations, complete and partial, uniform and nonuniform.

Author : Ya.G. Sinai
Publisher : Springer
Page : 304 pages
File Size : 47,5 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 3540170014

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Dynamical Systems II by Ya.G. Sinai Pdf

Following the concept of the EMS series this volume sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and to its applications to dynamical systems and statistical mechanics. The exposition starts from the basic of the subject, introducing ergodicity, mixing and entropy. Then the ergodic theory of smooth dynamical systems is presented - hyperbolic theory, billiards, one-dimensional systems and the elements of KAM theory. Numerous examples are presented carefully along with the ideas underlying the most important results. The last part of the book deals with the dynamical systems of statistical mechanics, and in particular with various kinetic equations. This book is compulsory reading for all mathematicians working in this field, or wanting to learn about it.

Author : D. V. Anosov
Publisher : Unknown
Page : 128 pages
File Size : 53,9 Mb
Release : 1988
Category : Celestial mechanics
ISBN : 0387570438

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Dynamical Systems by D. V. Anosov Pdf

Author : D.V. Anosov,V.I. Arnold,S.Kh. Aranson,I.U. Bronshtein,V.Z. Grines,Yu.S. Ilyashenko
Publisher : Springer
Page : 237 pages
File Size : 42,6 Mb
Release : 1994-06-01
Category : Mathematics
ISBN : 3540170006

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Dynamical Systems I by D.V. Anosov,V.I. Arnold,S.Kh. Aranson,I.U. Bronshtein,V.Z. Grines,Yu.S. Ilyashenko Pdf

From the reviews: "The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." Journal de Physique

Author : Vladimir Igorevich Arnolʹd
Publisher : Unknown
Page : 0 pages
File Size : 40,5 Mb
Release : 1988
Category : Mathematics
ISBN : 0387505830

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Dynamical Systems: Singularity theory I by Vladimir Igorevich Arnolʹd Pdf

1. Ordinary differential equations and smooth dynamical systems by D.V. Anosov, V.I. Arnold (eds.). 2. Ergodic theory with applications to dynamical systems an d statistical mechanics by Ya. G. Sinai (ed.). 3. [without special title]. 4. S ymplectic geometry and its applications by V.I. Arnold, S.P. Novikov (eds.).

Author : I︠A︡kov Grigorʹevich Sinaĭ,D. V. Anosov
Publisher : Nelson Thornes
Page : 290 pages
File Size : 45,7 Mb
Release : 1989
Category : Mathematics
ISBN : 3540181733

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Ergodic Theory with Applications to Dynamical Systems and Statistical Mechanics by I︠A︡kov Grigorʹevich Sinaĭ,D. V. Anosov Pdf

1. Ordinary differential equations and smooth dynamical systems by D.V. Anosov, V.I. Arnold (eds.). 2. Ergodic theory with applications to dynamical systems an d statistical mechanics by Ya. G. Sinai (ed.). 3. [without special title]. 4. S ymplectic geometry and its applications by V.I. Arnold, S.P. Novikov (eds.).

Author : Michael Brin,Boris Hasselblatt,Ya. B. Pesin
Publisher : Cambridge University Press
Page : 490 pages
File Size : 55,8 Mb
Release : 2004-08-16
Category : Mathematics
ISBN : 0521840732

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Modern Dynamical Systems and Applications by Michael Brin,Boris Hasselblatt,Ya. B. Pesin Pdf

This volume presents a broad collection of current research by leading experts in the theory of dynamical systems.

Author : D. V. Anosov,A. A. Bolibruch
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 41,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783322929099

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The Riemann-Hilbert Problem by D. V. Anosov,A. A. Bolibruch Pdf

The Riemann-Hilbert problem (Hilbert's 21st problem) belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concerns the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this turned out to be a rare case of a wrong forecast made by him. In 1989 the second author (A. B.) discovered a counterexample, thus obtaining a negative solution to Hilbert's 21st problem in its original form.

Author : Boris Hasselblatt,Anatole Katok
Publisher : Cambridge University Press
Page : 436 pages
File Size : 46,9 Mb
Release : 2003-06-23
Category : Mathematics
ISBN : 0521583047

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A First Course in Dynamics by Boris Hasselblatt,Anatole Katok Pdf

The theory of dynamical systems has given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introductory text covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The only prerequisite is a basic undergraduate analysis course. The authors use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.

Author : Vaughn Climenhaga,Anatole Katok
Publisher : American Mathematical Soc.
Page : 420 pages
File Size : 42,5 Mb
Release : 2017-04-07
Category : Geometry
ISBN : 9781470434793

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From Groups to Geometry and Back by Vaughn Climenhaga,Anatole Katok Pdf

Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.

Author : Luís Barreira,Yakov Pesin
Publisher : American Mathematical Society
Page : 355 pages
File Size : 53,7 Mb
Release : 2023-04-28
Category : Mathematics
ISBN : 9781470473075

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Introduction to Smooth Ergodic Theory by Luís Barreira,Yakov Pesin Pdf

This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. A detailed description of all the basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature, is also presented. There are more than 80 exercises. The book is aimed at graduate students specializing in dynamical systems and ergodic theory as well as anyone who wishes to get a working knowledge of smooth ergodic theory and to learn how to use its tools. It can also be used as a source for special topics courses on nonuniform hyperbolicity. The only prerequisite for using this book is a basic knowledge of real analysis, measure theory, differential equations, and topology, although the necessary background definitions and results are provided. In this second edition, the authors improved the exposition and added more exercises to make the book even more student-oriented. They also added new material to bring the book more in line with the current research in dynamical systems.

Author : A. B. Katok,Vaughn Climenhaga
Publisher : American Mathematical Soc.
Page : 307 pages
File Size : 44,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821846797

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Lectures on Surfaces by A. B. Katok,Vaughn Climenhaga Pdf

Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. This book introduces many of the principal actors - the round sphere, flat torus, Mobius strip, and Klein bottle.

Author : Vladimir I. Arnold,A.A. Bolibruch,Ludwig Faddeev,OSIPOV YURIY S.,Yakov G. Sinai,Yu. I. Manin,V.B. Filippov,Vladimir M. Tikhomirov,Anatoly M. Vershik
Publisher : Springer
Page : 0 pages
File Size : 40,7 Mb
Release : 2010-02-12
Category : Mathematics
ISBN : 3642062253

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Mathematical Events of the Twentieth Century by Vladimir I. Arnold,A.A. Bolibruch,Ludwig Faddeev,OSIPOV YURIY S.,Yakov G. Sinai,Yu. I. Manin,V.B. Filippov,Vladimir M. Tikhomirov,Anatoly M. Vershik Pdf

This book contains several contributions on the most outstanding events in the development of twentieth century mathematics, representing a wide variety of specialities in which Russian and Soviet mathematicians played a considerable role. The articles are written in an informal style, from mathematical philosophy to the description of the development of ideas, personal memories and give a unique account of personal meetings with famous representatives of twentieth century mathematics who exerted great influence in its development. This book will be of great interest to mathematicians, who will enjoy seeing their own specialities described with some historical perspective. Historians will read it with the same motive, and perhaps also to select topics for future investigation.

Author : Heather A. Harrington,Mohamed Omar,Matthew Wright
Publisher : American Mathematical Soc.
Page : 277 pages
File Size : 51,5 Mb
Release : 2017-03-16
Category : Commutative algebra -- Computational aspects and applications -- Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
ISBN : 9781470423216

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Algebraic and Geometric Methods in Discrete Mathematics by Heather A. Harrington,Mohamed Omar,Matthew Wright Pdf

This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics, held on January 11, 2015, in San Antonio, Texas. The papers present connections between techniques from “pure” mathematics and various applications amenable to the analysis of discrete models, encompassing applications of combinatorics, topology, algebra, geometry, optimization, and representation theory. Papers not only present novel results, but also survey the current state of knowledge of important topics in applied discrete mathematics. Particular highlights include: a new computational framework, based on geometric combinatorics, for structure prediction from RNA sequences; a new method for approximating the optimal solution of a sum of squares problem; a survey of recent Helly-type geometric theorems; applications of representation theory to voting theory and game theory; a study of fixed points of tensors; and exponential random graph models from the perspective of algebraic statistics with applications to networks. This volume was written for those trained in areas such as algebra, topology, geometry, and combinatorics who are interested in tackling problems in fields such as biology, the social sciences, data analysis, and optimization. It may be useful not only for experts, but also for students who wish to gain an applied or interdisciplinary perspective.

Author : Gregory Arone,Brenda Johnson,Pascal Lambrechts,Brian A. Munson,Ismar Volić
Publisher : American Mathematical Soc.
Page : 259 pages
File Size : 49,6 Mb
Release : 2017-01-24
Category : $K$-theory -- Higher algebraic $K$-theory -- Algebraic $K$-theory of spaces
ISBN : 9781470417000

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Manifolds and $K$-Theory by Gregory Arone,Brenda Johnson,Pascal Lambrechts,Brian A. Munson,Ismar Volić Pdf

This volume contains the proceedings of the conference on Manifolds, -Theory, and Related Topics, held from June 23–27, 2014, in Dubrovnik, Croatia. The articles contained in this volume are a collection of research papers featuring recent advances in homotopy theory, -theory, and their applications to manifolds. Topics covered include homotopy and manifold calculus, structured spectra, and their applications to group theory and the geometry of manifolds. This volume is a tribute to the influence of Tom Goodwillie in these fields.