Published 1991
by Springer-Verlag in Berlin, New York .
Written in English
Edition Notes
Includes bibliographical references.
| Statement | L. Arnold, H. Crauel, J.-P. Eckmann, eds. |
| Series | Lecture notes in mathematics ;, 1486, Lecture notes in mathematics (Springer-Verlag) ;, 1486. |
| Contributions | Arnold, L. 1937-, Crauel, H. 1956-, Eckmann, Jean Pierre. |
| Classifications | |
|---|---|
| LC Classifications | QA3 .L28 no. 1486, QA402 .L28 no. 1486 |
| The Physical Object | |
| Pagination | 365 p. : |
| Number of Pages | 365 |
| ID Numbers | |
| Open Library | OL1554073M |
| ISBN 10 | 3540546626, 0387546626 |
| LC Control Number | 91034152 |
A positive Lyapunov exponent measures or quantifies sensitive dependence on initial conditions by showing the average rate (as evaluated over the entire attractor) at which two close points separate with time. Some authors refer to a Lyapunov exponent as a Lyapunov characteristic exponent (LCE) or simply a characteristic exponent. LYAPUNOV EXPONENTS Figure A numerical computation of the loga-rithm of the stretch ˆn >(Jt Jt)ˆn in formula () for the Rössler flow (), plotted as a function of the Rössler time units. The slope is the leading Lyapunov exponent ˇ The exponent is positive, so numerics lends credence to the hypothesis that the Rössler File Size: KB. The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and. Lyapunov Exponents Proceedings of a Conference held in Oberwolfach, May 28 - June 2, Editors: Arnold, Ludwig, Crauel, Hans, Eckmann, Jean-Pierre (Eds.) Free Preview.
The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and Cited by: The Lyapunov exponents are hard to calculate in general and one needs to rely on numerical methods. Naive numerical evaluation of 1 A naive approach is to solve the dynamical system x_ = f(x) numerically for two trajectories starting at x(0) and x(0) + (0). 8. Lyapunov exponent; Bifurcation diagram; Poincaré Section; Chapter \(\) showed that motion in non-linear systems can exhibit both order and chaos. The transition between ordered motion and chaotic motion depends sensitively on both the initial conditions and the model parameters. In mathematics the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close tatively, two trajectories in phase space with initial separation vector diverge (provided that the divergence can be treated within the linearized approximation) at a rate given by.
setups. Moreover, on the basis of the Lyapunov exponent analysis, one can develop novel approaches to explore concepts such as hyperbolicity that previously appeared to be of purely mathematical nature. In this book we attempt to give a panoramic view of the world of Lyapunov exponents. 1. Introduction; 2. The basics; 3. Numerical methods; 4. Lyapunov vectors; 5. Fluctuations and generalized exponents; 6. Dimensions and dynamical entropies; 7. Finite. leading Lyapunov exponent requires rescaling the dis-tance in order to keep the nearby trajectory separation within the linearized flow range. δ x δ x δ x 2 x(t)1 1 x(0) 0 x(t)2 are {σ2 j}, the squares of principal stretches. example p. Lyapunov exponents (J. Mathiesen and P. Cvitanovic´) The mean growth rate of the distance. This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. It discusses the foundations and some of the main results and main techniques in the area, while also highlighting selected topics of current research interest.
