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Type: Artigo
Title: Topology of foliations and decomposition of stochastic flows of diffeomorphisms
Author: Melo, Alison M.
Morgado, Leandro
Ruffino, Paulo R.
Abstract: Let M be a compact manifold equipped with a pair of complementary foliations, say horizontal and vertical. In Catuogno et al. (Stoch Dyn 13(4):1350009, 2013) it is shown that, up to a stopping time ττ, a stochastic flow of local diffeomorphisms φtφt in M can be written as a Markovian process in the subgroup of diffeomorphisms which preserve the horizontal foliation composed with a process in the subgroup of diffeomorphisms which preserve the vertical foliation. Here, we discuss topological aspects of this decomposition. The main result guarantees the global decomposition of a flow if it preserves the orientation of a transversely orientable foliation. In the last section, we present an Itô-Liouville formula for subdeterminants of linearised flows. We use this formula to obtain sufficient conditions for the existence of the decomposition for all t≥0t≥0
Subject: Difeomorfismos
Fluxo estocástico
Folheações (Matemática)
Country: Estados Unidos
Editor: Springer
Citation: Journal Of Dynamics And Differential Equations. Springer New York Llc, p. 1 - 16, 2016.
Rights: fechado
Identifier DOI: 10.1007/s10884-016-9553-3
Date Issue: 2018
Appears in Collections:IMECC - Artigos e Outros Documentos

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