| Full text | |
| Author(s): |
Antunes, Andre Amaral
;
Carvalho, Tiago
;
Varao, Regis
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 362, p. 22-pg., 2023-03-13. |
| Abstract | |
Non-smooth vector fields do not have necessarily the property of uniqueness of solution passing through a point and this is responsible to enrich the behavior of the system. Even on the plane, non-smooth vector fields can be chaotic, a feature impossible for the smooth or continuous case. We propose a new approach to better understand chaos for non-smooth vector fields by using the notion of entropy of a system. We construct a metric space of all possible trajectories of a non-smooth vector field, where we define a flow inherited by the vector field and then define the topological entropy in this scenario. As a consequence, we are able to obtain some general results and give some examples of planar non-smooth vector fields with positive (finite and infinite) entropy.(c) 2023 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 19/10450-0 - Piecewise smooth vector fields: Closing Lemmas, shifts and horseshoe dynamics. |
| Grantee: | Tiago de Carvalho |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 16/22475-9 - Different contexts for chaos |
| Grantee: | José Régis Azevedo Varão Filho |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 19/10269-3 - Ergodic and qualitative theories of dynamical systems II |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 21/12395-6 - Piecewise smooth vector fields: theory and applications |
| Grantee: | Tiago de Carvalho |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 17/18255-6 - Closing lemmas and shifts for piecewise smooth vector fields |
| Grantee: | Andre do Amaral Antunes |
| Support Opportunities: | Scholarships in Brazil - Doctorate (Direct) |
| FAPESP's process: | 17/06463-3 - Probabilistic and algebraic aspects of smooth dynamical systems |
| Grantee: | Ali Tahzibi |
| Support Opportunities: | Research Projects - Thematic Grants |