Ebook: Lyapunov Exponents: Proceedings of a Conference held in Oberwolfach, May 28 – June 2, 1990

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.

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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.
Content:
Front Matter....Pages -
Random dynamical systems....Pages 1-22
Lyapunov exponents and asymptotic behaviour of the product of random matrices....Pages 23-37
Lyapunov exponents of random dynamical systems on grassmannians....Pages 38-50
Eigenvalue representation for the Lyapunov exponents of certain Markov processes....Pages 51-63
Analytic dependence of Lyapunov exponents on transition probabilities....Pages 64-80
A second order extension of Oseledets theorem....Pages 81-85
The upper Lyapunov exponent of Sl(2,R) cocycles: Discontinuity and the problem of positivity....Pages 86-97
Linear skew-product flows and semigroups of weighted composition operators....Pages 98-111
Filtre de Kalman Bucy et exposants de Lyapounov....Pages 112-122
Invariant measures for nonlinear stochastic differential equations....Pages 123-140
How to construct stochastic center manifolds on the level of vector fields....Pages 141-158
Additive noise turns a hyperbolic fixed point into a stationary solution....Pages 159-164
Lyapunov functions and almost sure exponential stability....Pages 165-177
Large deviations for random expanding maps....Pages 178-186
Multiplicative ergodic theorems in infinite dimensions....Pages 187-195
Stochastic flow and lyapunov exponents for abstract stochastic PDEs of parabolic type....Pages 196-205
The Lyapunov exponent for products of infinite-dimensional random matrices....Pages 206-215
Lyapunov exponents and complexity for interval maps....Pages 216-226
An inequality for the Ljapunov exponent of an ergodic invariant measure for a piecewise monotonic map of the interval....Pages 227-231
G?n?ralisation du th?or?me de Pesin pour l'?-entropie....Pages 232-242
Systems of classical interacting particles with nonvanishing Lyapunov exponents....Pages 243-262
Lyapunov exponents from time series....Pages 263-270
Lyapunov exponents in stochastic structural dynamics....Pages 271-291
Stochastic approach to small disturbance stability in power systems....Pages 292-308
Lyapunov exponents and invariant measures of equilibria and limit cycles....Pages 309-321
Sample stability of multi-degree-of-freedom systems....Pages 322-330
Lyapunov exponents of control flows....Pages 331-365

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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.
Content:
Front Matter....Pages -
Random dynamical systems....Pages 1-22
Lyapunov exponents and asymptotic behaviour of the product of random matrices....Pages 23-37
Lyapunov exponents of random dynamical systems on grassmannians....Pages 38-50
Eigenvalue representation for the Lyapunov exponents of certain Markov processes....Pages 51-63
Analytic dependence of Lyapunov exponents on transition probabilities....Pages 64-80
A second order extension of Oseledets theorem....Pages 81-85
The upper Lyapunov exponent of Sl(2,R) cocycles: Discontinuity and the problem of positivity....Pages 86-97
Linear skew-product flows and semigroups of weighted composition operators....Pages 98-111
Filtre de Kalman Bucy et exposants de Lyapounov....Pages 112-122
Invariant measures for nonlinear stochastic differential equations....Pages 123-140
How to construct stochastic center manifolds on the level of vector fields....Pages 141-158
Additive noise turns a hyperbolic fixed point into a stationary solution....Pages 159-164
Lyapunov functions and almost sure exponential stability....Pages 165-177
Large deviations for random expanding maps....Pages 178-186
Multiplicative ergodic theorems in infinite dimensions....Pages 187-195
Stochastic flow and lyapunov exponents for abstract stochastic PDEs of parabolic type....Pages 196-205
The Lyapunov exponent for products of infinite-dimensional random matrices....Pages 206-215
Lyapunov exponents and complexity for interval maps....Pages 216-226
An inequality for the Ljapunov exponent of an ergodic invariant measure for a piecewise monotonic map of the interval....Pages 227-231
G?n?ralisation du th?or?me de Pesin pour l'?-entropie....Pages 232-242
Systems of classical interacting particles with nonvanishing Lyapunov exponents....Pages 243-262
Lyapunov exponents from time series....Pages 263-270
Lyapunov exponents in stochastic structural dynamics....Pages 271-291
Stochastic approach to small disturbance stability in power systems....Pages 292-308
Lyapunov exponents and invariant measures of equilibria and limit cycles....Pages 309-321
Sample stability of multi-degree-of-freedom systems....Pages 322-330
Lyapunov exponents of control flows....Pages 331-365
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