Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/53342
Type: Artigo
Title: Matrix of rotation for stochastic dynamical systems
Title Alternative: 
Author: Ruffino, Paulo R.C.
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.
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.
metadata.dc.description.abstractalternative: 
Subject: Sistemas dinâmicos estocásticos
Matriz de rotação
Fibrados (Matemática)
Country: Alemanha
Editor: Springer
Citation: Computational & Applied Mathematics. Springer Heidelberg, v. 18, n. 2, n. 231, n. 245, 1999.
Rights: fechado
Identifier DOI: 0
Address: https://www.springer.com/journal/40314
Date Issue: 1999
Appears in Collections:IMECC - Artigos e Outros Documentos

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