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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.)

A note on invariant measures for Filippov systems

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Author(s):
Novaes, Douglas D. [1] ; Varao, Regis [1]
Total Authors: 2
Affiliation:
[1] Univ Estadual Campinas UNICAMP, Dept Matemat, Inst Matemat Estat & Comp Cient IMECC, Rua Sergio Buarque Holanda, 651, Cidade Univ Zeferi, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: BULLETIN DES SCIENCES MATHEMATIQUES; v. 167, MAR 2021.
Web of Science Citations: 0
Abstract

We are interested in Filippov systems which preserve a probability measure on a compact manifold. We define a measure to be invariant for a Filippov system as the natural analogous definition of invariant measure for flows. Our main result concerns Filippov systems which preserve a probability measure equivalent to the volume measure. As a consequence, the volume preserving Filippov systems are the refractive piecewise volume preserving ones. We conjecture that if a Filippov system admits an invariant probability measure, this measure does not see the trajectories where there is a break of uniqueness. We prove this conjecture for Lipschitz differential inclusions. Then, in light of our previous results, we analyze the existence of invariant measures for many examples of Filippov systems defined on compact manifolds. (C) 2021 Elsevier Masson SAS. All rights reserved. (AU)

FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
Grantee:Luiz Antonio Barrera San Martin
Support type: Research Projects - Thematic Grants
FAPESP's process: 17/06463-3 - Probabilistic and algebraic aspects of smooth dynamical systems
Grantee:Ali Tahzibi
Support type: Research Projects - Thematic Grants
FAPESP's process: 16/22475-9 - Different contexts for chaos
Grantee:José Régis Azevedo Varão Filho
Support type: Regular Research Grants