Topics In Ergodic Theory Pms 44 Volume 44

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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.

Etale Cohomology Pms 33

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Author : J. S. Milne
language : en
Publisher: Princeton University Press
Release Date : 1980-04-21

Etale Cohomology Pms 33 written by J. S. Milne 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 1980-04-21 with Mathematics categories.

One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and p-adic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to étale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and étale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of étale sheaves and elementary étale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in étale cohomology -- those of base change, purity, Poincaré duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general L-series. Originally published in 1980. 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.

Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane Pms 48

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Author : Kari Astala
language : en
Publisher: Princeton University Press
Release Date : 2009-01-18

Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane Pms 48 written by Kari Astala 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 2009-01-18 with Mathematics categories.

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.

New Trends In Stochastic Analysis And Related Topics

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Author : Huaizhong Zhao
language : en
Publisher: World Scientific
Release Date : 2011

New Trends In Stochastic Analysis And Related Topics written by Huaizhong Zhao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.

Ergodic Theory

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Author : I. P. Cornfeld
language : en
Publisher: Springer
Release Date : 2012-07-02

Ergodic Theory written by I. P. Cornfeld and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-02 with Mathematics categories.

Ergodic theory is one of the few branches of mathematics which has changed radically during the last two decades. Before this period, with a small number of exceptions, ergodic theory dealt primarily with averaging problems and general qualitative questions, while now it is a powerful amalgam of methods used for the analysis of statistical properties of dyna mical systems. For this reason, the problems of ergodic theory now interest not only the mathematician, but also the research worker in physics, biology, chemistry, etc. The outline of this book became clear to us nearly ten years ago but, for various reasons, its writing demanded a long period of time. The main principle, which we adhered to from the beginning, was to develop the approaches and methods or ergodic theory in the study of numerous concrete examples. Because of this, Part I of the book contains the description of various classes of dynamical systems, and their elementary analysis on the basis of the fundamental notions of ergodicity, mixing, and spectra of dynamical systems. Here, as in many other cases, the adjective" elementary" i~ not synonymous with "simple. " Part II is devoted to "abstract ergodic theory. " It includes the construc tion of direct and skew products of dynamical systems, the Rohlin-Halmos lemma, and the theory of special representations of dynamical systems with continuous time. A considerable part deals with entropy.

Bulletin New Series Of The American Mathematical Society

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Author :
language : en
Publisher:
Release Date : 2007

Bulletin New Series Of The American Mathematical Society written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Concepts And Results In Chaotic Dynamics A Short Course

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Author : Pierre Collet
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-26

Concepts And Results In Chaotic Dynamics A Short Course written by Pierre Collet 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 2006-10-26 with Mathematics categories.

The study of dynamical systems is a well established field. This book provides a panorama of several aspects of interest to mathematicians and physicists. It collects the material of several courses at the graduate level given by the authors, avoiding detailed proofs in exchange for numerous illustrations and examples. Apart from common subjects in this field, a lot of attention is given to questions of physical measurement and stochastic properties of chaotic dynamical systems.

Chaos Concepts Control And Constructive Use

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Author : Yurii Bolotin
language : en
Publisher: Springer
Release Date : 2016-10-24

Chaos Concepts Control And Constructive Use written by Yurii Bolotin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-24 with Science categories.

This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.

Contemporary Economic Issues

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Author : Murat Sertel
language : en
Publisher: Springer
Release Date : 2016-01-01

Contemporary Economic Issues written by Murat Sertel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-01 with Business & Economics categories.

A guide to the experiences of economic reform since the second World War, and system reform and economic integration across the world in the past decade. The first part of the book examines why only a small number of developing countries have succeeded in their modernization attempts this century. What lessons can be learnt from the successes of the East Asian NIEs and failures of other economies to emulate them? The very different experiences of the transition to market economies in the former socialist countries of Eastern Europe and China is the focus of the next section, with comparisons drawn with the Latin American reform experience, especially in Chile. The effects of economic integration schemes are examined in the final sector, with case-studies of Tunisia and Morocco's Free Trade Agreements with the EU, and of economic integration and the Arab-Israeli peace process.

Topics In Groups And Geometry

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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Springer Nature
Release Date : 2022-01-01

Topics In Groups And Geometry written by Tullio Ceccherini-Silberstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.

This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.