Normal forms for random diffeomorphisms
type: Item
instance of: scholarly article
title: Normal forms for random diffeomorphisms
zbMATH Open document ID: 0763.34026
DOI: 10.1007/BF01053806
author: Ludwig Arnold
author: Kedai Xu
published in: Journal of Dynamics and Differential Equations
publication date: 1993-01-16T00:00:00Z
review text: The stochastic normal forms theory is developed to make random diffeomorphism as simple as possible by means of a nonlinear random coordinate transform. Stochastic versions of Lyapunov exponents and eigenspaces are introduced using Oseledec multiplicative ergodic theorem. The stochastic analogues of resonance and average are studied. No assumptions about the smallness of random perturbations are made. The unified approach presented here covers the case of stochastic differential equations as well as random difference equations. The equation eliminating nonlinear terms is infinite-dimensional.
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 34D08
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 94579
zbMATH Keywords: stochastic normal forms theory
zbMATH Keywords: random diffeomorphism
zbMATH Keywords: nonlinear random coordinate transform
zbMATH Keywords: Lyapunov exponents
zbMATH Keywords: eigenspaces
zbMATH Keywords: Oseledec multiplicative ergodic theorem
zbMATH Keywords: resonance
zbMATH Keywords: average
zbMATH Keywords: random perturbations
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: random difference equations
reviewed by: R. Mikulevicius
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 94579