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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.)

Minimal sets and chaos in planar piecewise smooth vector fields

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Author(s):
Carvalho, Tiago [1] ; Euzebio, Rodrigo Donizete [2]
Total Authors: 2
Affiliation:
[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
Total Affiliations: 2
Document type: Journal article
Source: Electronic Journal of Qualitative Theory of Differential Equations; n. 33, p. 1-15, 2020.
Web of Science Citations: 10
Abstract

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)

FAPESP's process: 19/10450-0 - Piecewise smooth vector fields: Closing Lemmas, shifts and horseshoe dynamics.
Grantee:Tiago de Carvalho
Support type: Regular Research Grants
FAPESP's process: 17/00883-0 - Piecewise smooth vector fields with applications in biology
Grantee:Tiago de Carvalho
Support type: Regular Research Grants