A note on invariant measures for Filippov systems

Autor(es)

Novaes, Douglas D. ^[1] ; Varao, Regis ^[1]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN DES SCIENCES MATHEMATIQUES; v. 167, MAR 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 18/13481-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 17/06463-3 - Aspectos probabilísticos e algébricos de sistemas dinâmicos suaves
• Beneficiário: Ali Tahzibi
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 16/22475-9 - Diferentes contextos para o caos
• Beneficiário: José Régis Azevedo Varão Filho
• Modalidade de apoio: Auxílio à Pesquisa - Regular