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Full Description
Since the predecessor to this volume (LNM 1186, Eds. L. Arnold, V. Wihstutz)appeared in 1986, significant progress has been made in the theory and applications of Lyapunov exponents - one of the key concepts of dynamical systems - and in particular, pronounced shifts towards nonlinear and infinite-dimensional systems and engineering applications are observable. This volume opens with an introductory survey article (Arnold/Crauel) followed by 26 original (fully refereed) research papers, some of which have in part survey character. From the Contents: L. Arnold, H. Crauel: Random Dynamical Systems.- I.Ya. Goldscheid: Lyapunov exponents and asymptotic behaviour of the product of random matrices.- Y. Peres: Analytic dependence of Lyapunov exponents on transition probabilities.- O. Knill: The upper Lyapunov exponent of Sl (2, R) cocycles:Discontinuity and the problem of positivity.- Yu.D. Latushkin, A.M. Stepin: Linear skew-product flows and semigroups of weighted composition operators.- P. Baxendale: Invariant measures for nonlinear stochastic differential equations.- Y. Kifer: Large deviationsfor random expanding maps.- P.
Thieullen: Generalisation du theoreme de Pesin pour l' -entropie.- S.T. Ariaratnam, W.-C. Xie: Lyapunov exponents in stochastic structural mechanics.- F. Colonius, W. Kliemann: Lyapunov exponents of control flows.
Contents
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.
