| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Journal of Dynamics and Differential Equations; v. 30, n. 1, p. 39-54, MAR 2018. |
| Web of Science Citations: | 0 |
| 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 , a stochastic flow of local diffeomorphisms 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 It-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. (AU) | |
| FAPESP's process: | 11/50151-0 - Dynamical phenomena in complex networks: fundamentals and applications |
| Grantee: | Elbert Einstein Nehrer Macau |
| Support type: | Research Projects - Thematic Grants |
| FAPESP's process: | 11/14797-2 - Stochastic dynamics in foliated spaces |
| Grantee: | Leandro Batista Morgado |
| Support type: | Scholarships in Brazil - Doctorate (Direct) |
| FAPESP's process: | 12/18780-0 - Geometry of control systems, dynamical and stochastics systems |
| Grantee: | Marco Antônio Teixeira |
| Support type: | Research Projects - Thematic Grants |