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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Topology of Foliations and Decomposition of Stochastic Flows of Diffeomorphisms

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Author(s):
Melo, Alison M. [1] ; Morgado, Leandro [1] ; Ruffino, Paulo R. [1]
Total Authors: 3
Affiliation:
[1] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 1
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