hains in 3D Filippov systems: A chaotic phenomeno

Autor(es)

Gomide, Otavio M. L. ^[1] ; Teixeira, Marco A. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Goias, Dept Math, IME, BR-74690900 Goiania, Go - Brazil

^[2] Univ Estadual Campinas, Dept Math, IMECC, BR-13083970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES; v. 159, p. 168-195, MAR 2022.
• Citações Web of Science: 0

Resumo

This work is devoted to the study of global connections between typical generic singularities, named T-singularities, in piecewise smooth dynamical systems. Such a singularity presents the so-called nonsmooth diabolo, which consists on a pair of invariant cones emanating from it. We analyze global features arising from the communication between the branches of a nonsmooth diabolo of a T-singularity and we prove that, under generic conditions, such communication leads to a chaotic behavior of the system. More specifically, we relate crossing orbits of a Filippov system presenting certain crossing self-connections to a T-singularity, with a Smale horseshoe of a first return map associated to the system. The techniques used in this work rely on the detection of transverse intersections between invariant manifolds of a hyperbolic fixed point of saddle type of such a first return map and the analysis of the Smale horseshoe associated to it. From the specific case discussed in our approach, we present a robust chaotic phenomenon for which its counterpart in the smooth case seems to happen only for highly degenerate systems. (C) 2021 Elsevier Masson SAS. All rights reserved. (AU)

• Processo FAPESP: 19/01682-4 - Dinâmica Global de Equações Diferenciais
• Beneficiário: Otávio Marçal Leandro Gomide
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• 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