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Type: Artigo de periódico
Title: Matrix of rotation for stochastic dynamical systems
Author: Ruffino, PRC
Abstract: The concept of matrix of rotation generalizes the rotation number for stochastic dynamical systems given in [11]. This matrix is the asymptotic time average of the Maurer-Cartan form composed with the Riemannian connection along the induced trajectory in the orthonormal frame bundle OM over an n-dimensional Riemannian manifold M. It provides the asymptotic behaviour of an orthonormal n-frame under the action of the derivative flow and the Gram-Schmidt orthonormalization. We lift the stochastic differential equation of the system on M to a stochastic differential equation in OM and we use Furstenberg-Khasminskii argument to prove that the matrix of rotation exists almost surely with respect to invariant measures on this bundle.
Subject: Stochastic dynamical systems
matrix of rotation
orthonormal frame bundle
Country: Alemanha
Editor: Springer Heidelberg
Rights: aberto
Date Issue: 1999
Appears in Collections:Unicamp - Artigos e Outros Documentos

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