A nonrandom lyapunov spectrum for nonlinear stochastic dynamical systems
作者:
Andrew Carverhill,
期刊:
Stochastics
(Taylor Available online 1986)
卷期:
Volume 17,
issue 4
页码: 253-287
ISSN:0090-9491
年代: 1986
DOI:10.1080/17442508608833393
出版商: Gordon and Breach, Science Publishers, Inc
关键词: Stochastic dynamical system;Lyapunov spectrum;multiplicative ergodic theorem;derivative system;random diffeomorphisms
数据来源: Taylor
摘要:
We present a nonrandom version of the Multiplicative Ergodic (Oseledec) Theorem for a nonlinear stochastic dynamical system on a smooth compact Riemannian Manifold M. This theorem characterises the a.s. asymptotic behaviour of the derivative system. Our approach (based on work of Furstenberg and Kifer, who deal with a linear system) is to consider an associated system on the projective bundle over M and to relate the behaviour of the theorem to the ergodic behaviour of this system. When the system has no random element, our work reduces to an alternative approach to the Multiplicative Ergodic Theorem for a diffeomorphism of M.
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