Dynamics Beyond Uniform Hyperbolicity A Global Geometric and Probabi
In broad terms, the goal of dynamics is to describe the long-term evolution of systems for which an "infinitesimal" evolution rule, such as a differential equation or the iteration of a map, is known. The notion of uniform hyperbolicity, introduced by Ste
- PDF / 20,761,491 Bytes
- 389 Pages / 439 x 666 pts Page_size
- 56 Downloads / 152 Views
Christian Bonatti Lorenzo J. Diaz Marcelo Viana
Dynamics Beyond Uniform Hyperbolicity A Global Geometric and Probabilistic Perspective
4y Springer
Authors Christian Bonatti Institut de Mathematiques de Bourgogne UMR5584duCNRS Universite de Bourgogne B.P. 47870 21078 Dijon Cedex France e-mail: [email protected]
Lorenzo J. Diaz Departamento de Matematica, PUC-Rio Rua Marques de Sao Vicente, 225 Edificio Cardeal Leme Gavea - Rio de Janeiro Brazil 22453-900
e-mail: [email protected]
Marcelo Viana IMPA Estrada Dona Castorina, 110 Jardim Botanico - Rio de Janeiro Brazil 22460-320
e-mail: [email protected]
Founding editor of the Encyclopaedia of Mathematical Sciences: R. V. Gamkrelidze Mathematics Subject Classification (2000): 37XX, 37CXX, 37DXX, 37EXX ISSN 0938-0396 ISBN 3-540-22066-6 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: by the authors using a Springer KT^X macro package Production: LE-TgX Jelonek, Schmidt & Vockler GbR, Leipzig Cover Design: E. Kirchner, Heidelberg, Germany Printed on acid-free paper 46/3142 YL 543210
To IMPA, for bringing us together.
Preface
What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to mention just a few. These systems have in common the fact that each possible state may be described by a finite (or infinite) number of observable quantities, like position, velocity, temperature, concentration, population density, and the like. Thus, the space of states (phase space) is a subset M of an Euclidean space Mm. Usually, there are some constraints between these quantities: for instance, for ideal gases pressure times volume must be proportional to temperature. Then the space M is often a manifold, an n-dimensional surface for some n < m. For continuous time systems, the evolution rule may be a differential equat
Data Loading...
