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Topology of Foliations and Decomposition of Stochastic Flows of Diffeomorphisms.
- Source :
-
Journal of Dynamics & Differential Equations . Mar2018, Vol. 30 Issue 1, p39-54. 16p. - Publication Year :
- 2018
-
Abstract
- Let <italic>M</italic> be a compact manifold equipped with a pair of complementary foliations, say horizontal and vertical. In Catuogno et al. (Stoch Dyn 13(4):1350009, <xref>2013</xref>) it is shown that, up to a stopping time τ<inline-graphic></inline-graphic>, a stochastic flow of local diffeomorphisms φt<inline-graphic></inline-graphic> in <italic>M</italic> 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≥0<inline-graphic></inline-graphic>. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10407294
- Volume :
- 30
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Dynamics & Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 128291851
- Full Text :
- https://doi.org/10.1007/s10884-016-9553-3