Artículos de revistas
Topology Of Foliations And Decomposition Of Stochastic Flows Of Diffeomorphisms
Registro en:
Journal Of Dynamics And Differential Equations. Springer New York Llc, p. 1 - 16, 2016.
1040-7294
10.1007/s10884-016-9553-3
2-s2.0-84991717374
Autor
Melo A.M.
Morgado L.
Ruffino P.R.
Institución
Resumen
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 (Formula presented.), a stochastic flow of local diffeomorphisms (Formula presented.) 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 (Formula presented.). © 2016 Springer Science+Business Media New York 1 16