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|Title:||Topology of foliations and decomposition of stochastic flows of diffeomorphisms|
|Author:||Melo, Alison M.|
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|
|Citation:||Journal Of Dynamics And Differential Equations. Springer New York Llc, p. 1 - 16, 2016.|
|Appears in Collections:||IMECC - Artigos e Outros Documentos|
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