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|Type:||Artigo de periódico|
|Title:||Matrix of rotation for stochastic dynamical systems|
|Abstract:||The concept of matrix of rotation generalizes the rotation number for stochastic dynamical systems given in . 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
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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