Minimal sets and chaos in planar piecewise smooth vector fields

Autor(es)

Carvalho, Tiago ^[1] ; Euzebio, Rodrigo Donizete ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Fac Filosofia Ciencias & Letras Ribeirao Preto, Dept Comp & Matemat, Av Bandeirantes, BR-14098322 Ribeirao Preto, SP - Brazil

^[2] IME UFG, Dept Matemat, Campus Samambaia, BR-74001970 Goiania, Go - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Electronic Journal of Qualitative Theory of Differential Equations; n. 33, p. 1-15, 2020.
• Citações Web of Science: 10

Resumo

Some aspects concerning chaos and minimal sets in discontinuous dynamical systems are addressed. The orientability dependence of trajectories sliding trough some variety is exploited and new phenomena emerging from this situation are highlighted. In particular, although chaotic flows and nontrivial minimal sets are not allowed for smooth vector fields in the plane, the existence of such objects for some classes of vector fields is verified. A characterization of chaotic flows in terms of orientable minimal sets is also provided. The main feature of the dynamical systems under study is related to the non uniqueness of trajectories in some zero measure region as well as the orientation of orbits reaching such region. (AU)

• Processo FAPESP: 17/00883-0 - Campos vetoriais suaves por partes com aplicações em problemas biológicos
• Beneficiário: Tiago de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 19/10450-0 - Campos vetoriais suaves por partes: Closing Lemmas, shifts e dinâmicas do tipo ferradura.
• Beneficiário: Tiago de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Regular