| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Univ Fed Goias, Dept Math, IME, BR-74690900 Goiania, Go - Brazil
[2] Univ Estadual Campinas, Dept Math, IMECC, BR-13083970 Campinas, SP - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES; v. 159, p. 168-195, MAR 2022. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 19/01682-4 - Global Dynamics of Differential Equations |
| Grantee: | Otávio Marçal Leandro Gomide |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 18/13481-0 - Geometry of control, dynamical and stochastic systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |