Dynamical Properties Of Diffeomorphisms Of The Annulus And Of The Torus
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Dynamical Properties Of Diffeomorphisms Of The Annulus And Of The Torus
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Author : Patrice Le Calvez
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Dynamical Properties Of Diffeomorphisms Of The Annulus And Of The Torus written by Patrice Le Calvez 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 2000 with Mathematics categories.
Originally published in French by the Societe Mathematique de France, in 1991, as volume 204 in the Asterisque series. The first chapter presents a survey of the theory of monotone twist maps of the annulus. The second generalizes some aspects of Aubry-Mather theory to such maps and presents a version of the Poincare-Birkhoff theorem in which the periodic orbits have the same braid type as in the linear case. Annotation copyrighted by Book News, Inc., Portland, OR
Topics In Dynamics And Ergodic Theory
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Author : Sergey Bezuglyi
language : en
Publisher: Cambridge University Press
Release Date : 2003-12-08
Topics In Dynamics And Ergodic Theory written by Sergey Bezuglyi 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 2003-12-08 with Mathematics categories.
This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups.
Complex Dynamics And Geometry
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Author : Dominique Cerveau
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Complex Dynamics And Geometry written by Dominique Cerveau 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.
In the last twenty years, the theory of holomorphic dynamical systems has had a resurgence of activity, particularly concerning the fine analysis of Julia sets associated with polynomials and rational maps in one complex variable. At the same time, closely related theories have had a similar rapid development, for example the qualitative theory of differential equations in the complex domain. The meeting, ``Etat de la recherche'', held at Ecole Normale Superieure de Lyon, presented the current state of the art in this area, emphasizing the unity linking the various sub-domains. This volume contains four survey articles corresponding to the talks presented at this meeting. D. Cerveau describes the structure of polynomial differential equations in the complex plane, focusing on the local analysis in neighborhoods of singular points. E. Ghys surveys the theory of laminations by Riemann surfaces which occur in many dynamical or geometrical situations. N. Sibony describes the present state of the generalization of the Fatou-Julia theory for polynomial or rational maps in two or more complex dimensions. Lastly, the talk by J.-C. Yoccoz, written by M. Flexor, considers polynomials of degree $2$ in one complex variable, and in particular, with the hyperbolic properties of these polynomials centered around the Jakobson theorem. This is a general introduction that gives a basic history of holomorphic dynamical systems, demonstrating the numerous and fruitful interactions among the topics. In the spirit of the ``Etat de la recherche de la SMF'' meetings, the articles are written for a broad mathematical audience, especially students or mathematicians working in different fields. This book is translated from the French edition by Leslie Kay.
An Initiation To Logarithmic Sobolev Inequalities
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Author : Gilles Royer
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
An Initiation To Logarithmic Sobolev Inequalities written by Gilles Royer 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 2007 with Mathematics categories.
This book provides an introduction to logarithmic Sobolev inequalities with some important applications to mathematical statistical physics. Royer begins by gathering and reviewing the necessary background material on selfadjoint operators, semigroups, Kolmogorov diffusion processes, solutions of stochastic differential equations, and certain other related topics. There then is a chapter on log Sobolev inequalities with an application to a strong ergodicity theorem for Kolmogorov diffusion processes. The remaining two chapters consider the general setting for Gibbs measures including existence and uniqueness issues, the Ising model with real spins and the application of log Sobolev inequalities to show the stabilization of the Glauber-Langevin dynamic stochastic models for the Ising model with real spins. The exercises and complements extend the material in the main text to related areas such as Markov chains. Information for our distributors: Titles in this series are co-published with Societe Mathematique de France. SMF members are entitled to AMS member discounts.
Hamiltonian Systems And Their Integrability
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Author : Mich'le Audin
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Hamiltonian Systems And Their Integrability written by Mich'le Audin 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 2008 with Mathematics categories.
Hamiltonian systems began as a mathematical approach to the study of mechanical systems. As the theory developed, it became clear that the systems that had a sufficient number of conserved quantities enjoyed certain remarkable properties. These are the completely integrable systems. In time, a rich interplay arose between integrable systems and other areas of mathematics, particularly topology, geometry, and group theory.This book presents some modern techniques in the theory of integrable systems viewed as variations on the theme of action-angle coordinates. These techniques include analytical methods coming from the Galois theory of differential equations, as well as more classical algebro-geometric methods related to Lax equations. Audin has included many examples and exercises. Most of the exercises build on the material in the text. None of the important proofs have been relegated to the exercises. Many of the examples are classical, rather than abstract. This book would be suitable for a graduate course in Hamiltonian systems.
Asymptotically Symmetric Einstein Metrics
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Author : Olivier Biquard
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Asymptotically Symmetric Einstein Metrics written by Olivier Biquard 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 2006 with Mathematics categories.
The correspondence between Einstein metrics and their conformal boundaries has recently been the focus of great interest. This is particularly so in view of the relation with the physical theory of the AdS/CFT correspondence. In this book, this correspondence is seen in the wider context of asymptotically symmetric Einstein metrics, that is Einstein metrics whose curvature is asymptotic to that of a rank one symmetric space. There is an emphasis on the correspondence between Einstein metrics and geometric structures on their boundary at infinity: conformal structures, CR structures, and quaternionic contact structures introduced and studied in the book. Two new constructions of such Einstein metrics are given, using two different kinds of techniques: analytic methods to construct complete Einstein metrics, with a unified treatment of all rank one symmetric spaces, relying on harmonic analysis; algebraic methods (twistor theory) to construct local solutions of the Einstein equation near the boundary.
Handbook Of Topological Fixed Point Theory
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Author : Robert F. Brown
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-10
Handbook Of Topological Fixed Point Theory written by Robert F. Brown 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 2005-06-10 with Mathematics categories.
This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.
The Schur Algorithm Reproducing Kernel Spaces And System Theory
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Author : Daniel Alpay
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
The Schur Algorithm Reproducing Kernel Spaces And System Theory written by Daniel Alpay 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 2001 with Computers categories.
Looks at matrix-valued Schur functions and their applications from the unifying point of view of space with reproducing kernels to study the relationship between the modeling of time-invariant dissipative linear systems and the theory of linear operators. Chapters cover reproducing kernel spaces, theory of linear systems, the Schur algorithm and the inverse scattering problem, operator models, interpolation, the indefinite case, the non-stationary case, and Riemann surfaces. Originally published in French by Societe Mathematique de France, 1998. Translated from the French by Stephen S. Wilson. Author information is not given. c. Book News Inc.
The Hyperbolization Theorem For Fibered 3 Manifolds
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Author : Jean-Pierre Otal
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
The Hyperbolization Theorem For Fibered 3 Manifolds written by Jean-Pierre Otal 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 2001 with Mathematics categories.
For graduate students familiar with low-dimensional topology and researchers in geometry and topology, Otal (CNRS-UMR 128, Lyon) offers a complete proof of Thurston's hyperbolization theorem for 3-manifolds that fiber as surface bundles. The original Le Theoreme d'Hyperbolisation pour les Varietes de Dimension 3, published by the French Mathematical Society in 1996, has been translated by Leslie D. Kay. c. Book News Inc.
Introduction To Hodge Theory
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Author : José Bertin
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Introduction To Hodge Theory written by José Bertin 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 2002 with Mathematics categories.
Hodge theory originated as an application of harmonic theory to the study of the geometry of compact complex manifolds. The ideas have proved to be quite powerful, leading to fundamentally important results throughout algebraic geometry. This book consists of expositions of various aspects of modern Hodge theory. Its purpose is to provide the nonexpert reader with a precise idea of the current status of the subject. The three chapters develop distinct but closely related subjects: $L^2$ Hodge theory and vanishing theorems; Frobenius and Hodge degeneration; variations of Hodge structures and mirror symmetry.The techniques employed cover a wide range of methods borrowed from the heart of mathematics: elliptic PDE theory, complex differential geometry, algebraic geometry in characteristic $p$, cohomological and sheaf-theoretic methods, deformation theory of complex varieties, Calabi-Yau manifolds, singularity theory, etc. A special effort has been made to approach the various themes from their most natural starting points. Each of the three chapters is supplemented with a detailed introduction and numerous references. The reader will find precise statements of quite a number of open problems that have been the subject of active research in recent years. The reader should have some familiarity with differential and algebraic geometry, with other prerequisites varying by chapter. The book is suitable as an accompaniment to a second course in algebraic geometry.