Examines all significant recent progress made in the theory and applications of a key component of dynamical systems, known as the Lyapunov exponents. Emphasis is placed on shifts towards nonlinear and infinite-dimensional systems and observable engineering applications.
Examines all significant recent progress made in the theory and applications of a key component of dynamical systems, known as the Lyapunov exponents....
Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an interesting mathematical structure going far beyond the simple equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimentally controllable parameter, there is a corresponding mathematical structure revealing a great deal about interrelations between the behavior for different parameter values.
This work explains some of the early results of this theory to mathematicians and theoretical physicists,...
Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an inte...
This book is devoted to the subject commonly called Chaotic Dynamics, namely the study of complicated behavior in time of maps and ?ows, called dynamical systems. The theory of chaotic dynamics has a deep impact on our understanding of - ture, and we sketch here our view on this question. The strength of this theory comes from its generality, in that it is not limited to a particular equation or scienti?c - main. It should be viewed as a conceptual framework with which one can capture properties of systems with complicated behavior. Obviously, such a general fra- work cannot describe a system...
This book is devoted to the subject commonly called Chaotic Dynamics, namely the study of complicated behavior in time of maps and ?ows, called dynami...
The physics of extended systems is a topic of great interest for the experimentalist and the theoretician alike. There exists a large literature on this subject in which solutions, bifurcations, fronts, and the dynamical stability of these objects are discussed. To the uninitiated reader, the theoretical methods that lead to the various results often seem somewhat ad hoc, and it is not clear how to generalize them to the nextthat is, not yet solvedproblem. In an introduction to the subject of instabilities in spatially infinite systems, Pierre Collet and Jean-Pierre Eckmann aim to give a...
The physics of extended systems is a topic of great interest for the experimentalist and the theoretician alike. There exists a large literature on...
