| Full text | |
| Author(s): |
Total Authors: 2
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| 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
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| 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: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 17/06463-3 - Probabilistic and algebraic aspects of smooth dynamical systems |
| Grantee: | Ali Tahzibi |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 16/22475-9 - Different contexts for chaos |
| Grantee: | José Régis Azevedo Varão Filho |
| Support Opportunities: | Regular Research Grants |