Lyapunov Exponents: Proceedings of a Conference Held in Oberwolfach, May 28 - June 2, 1990

ISBN-13: 9783540546627 / Angielski / Miękka / 1991 / 368 str.

Ludwig Arnold; Hans Crauel; Jean-Pierre Eckmann

Opis

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.

Spis treści

Random dynamical systems.- Lyapunov exponents and asymptotic behaviour of the product of random matrices.- Lyapunov exponents of random dynamical systems on grassmannians.- Eigenvalue representation for the Lyapunov exponents of certain Markov processes.- Analytic dependence of Lyapunov exponents on transition probabilities.- A second order extension of Oseledets theorem.- The upper Lyapunov exponent of Sl(2,R) cocycles: Discontinuity and the problem of positivity.- Linear skew-product flows and semigroups of weighted composition operators.- Filtre de Kalman Bucy et exposants de Lyapounov.- Invariant measures for nonlinear stochastic differential equations.- How to construct stochastic center manifolds on the level of vector fields.- Additive noise turns a hyperbolic fixed point into a stationary solution.- Lyapunov functions and almost sure exponential stability.- Large deviations for random expanding maps.- Multiplicative ergodic theorems in infinite dimensions.- Stochastic flow and lyapunov exponents for abstract stochastic PDEs of parabolic type.- The Lyapunov exponent for products of infinite-dimensional random matrices.- Lyapunov exponents and complexity for interval maps.- An inequality for the Ljapunov exponent of an ergodic invariant measure for a piecewise monotonic map of the interval.- Généralisation du théorème de Pesin pour l'?-entropie.- Systems of classical interacting particles with nonvanishing Lyapunov exponents.- Lyapunov exponents from time series.- Lyapunov exponents in stochastic structural dynamics.- Stochastic approach to small disturbance stability in power systems.- Lyapunov exponents and invariant measures of equilibria and limit cycles.- Sample stability of multi-degree-of-freedom systems.- Lyapunov exponents of control flows.