Lyapunov Exponents: Proceedings of a Workshop held in Bremen, November 12-15, 1984

ISBN-13: 9783540164586 / Angielski / Miękka / 1986 / 378 str.

Ludwig Arnold;Volker Wihstutz

Opis

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.

Spis treści

Lyapunov exponents: A survey.- Oscillation des produits de matrices aleatoires dont l'exposant de lyapounov est nul.- Unique ergodicity and random matrix products.- Positivity of the exponent for stationary sequences of matrices.- Characteristic exponents for random homeomorphisms of metric spaces.- Lyapunov exponents of linear stochastic systems.- Addendum a note on transitivity of coupled control systems.- Almost sure and moment stability for linear ito equations.- Almost sure instability of a class of linear stochastic systems with jump process coefficients.- On a generalization of the Lyapunov exponent of a second order linear stochastic differential equation.- Parameter dependence of the Lyapunov exponent for linear stochastic systems. A survey.- An example concerning the geometric significance of the rotation number — integrated density of states.- Lyapunov exponents for schrödinger operators with random, but deterministic potentials.- Lyapunov exponents and one-dimensional alloys.- Resonance states in disordered systems.- The Lyapounov index, the density of states and their regularity for general stochastic potentials.- Computations of the sum of positive Lyapunov exponents for the Lloyd model in a strip.- Statistics of reflected pulses.- Lyapunov exponents and invariant measures of stochastic systems on manifolds.- Survey: Lyapunov exponents for stochastic flows on manifolds.- Bounds for average Lyapunov exponents of gradient stochastic systems.- The Lyapunov spectrum of a stochastic flow of diffeomorphisms.- Lyapunov exponents and phase transitions in dynamical systems.- Coupling sensitivity and cliff in chaotic dynamics.