Minimal sets and chaos in planar piecewise smooth vector fields
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2020-05-01
|
| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7661 |
| _version_ | 1797830522167099392 |
|---|---|
| author | Tiago Carvalho Rodrigo Euzébio |
| author_facet | Tiago Carvalho Rodrigo Euzébio |
| author_sort | Tiago Carvalho |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T13:37:26Z |
| format | Article |
| id | doaj.art-8c8d3ffec5e94d858ecbdff5b496b8ba |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:26Z |
| publishDate | 2020-05-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-8c8d3ffec5e94d858ecbdff5b496b8ba2023-05-09T07:53:10ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752020-05-0120203311510.14232/ejqtde.2020.1.337661Minimal sets and chaos in planar piecewise smooth vector fieldsTiago Carvalho0Rodrigo Euzébio1Universidade de São Paulo, BrazilUniversidade Federal de Goias, Goiânia, BrazilSome 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.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7661vector fieldspiecewise smooth vector fieldschaosminimal sets |
| spellingShingle | Tiago Carvalho Rodrigo Euzébio Minimal sets and chaos in planar piecewise smooth vector fields Electronic Journal of Qualitative Theory of Differential Equations vector fields piecewise smooth vector fields chaos minimal sets |
| title | Minimal sets and chaos in planar piecewise smooth vector fields |
| title_full | Minimal sets and chaos in planar piecewise smooth vector fields |
| title_fullStr | Minimal sets and chaos in planar piecewise smooth vector fields |
| title_full_unstemmed | Minimal sets and chaos in planar piecewise smooth vector fields |
| title_short | Minimal sets and chaos in planar piecewise smooth vector fields |
| title_sort | minimal sets and chaos in planar piecewise smooth vector fields |
| topic | vector fields piecewise smooth vector fields chaos minimal sets |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7661 |
| work_keys_str_mv | AT tiagocarvalho minimalsetsandchaosinplanarpiecewisesmoothvectorfields AT rodrigoeuzebio minimalsetsandchaosinplanarpiecewisesmoothvectorfields |