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| Author(s): |
André do Amaral Antunes
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São José do Rio Preto. 2021-03-11. |
| Institution: | Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto |
| Defense date: | 2021-02-25 |
| Advisor: | Tiago de Carvalho |
| Abstract | |
Recently, the theory concerning piecewise smooth vector fields (PSVFs for short) has been undergoing important improvements. One line of investigation of these vector fields is to seek to establish results analogous to those already well known for the smooth case, such as Poincaré Bendixson and Poincaré Index Theorems. On this line of work, we tackle the classical problem of Closing Lemma in the setting of PSVFs and provide a positive answer for the case C0. Another possible line of investigation is studying the differences between PSVFs and smooth vector fields. Most of them arises from the fact that there is no uniqueness of trajectory passing through a point for a PSVF. It implies results like the existence of a planar PSVF that is chaotic. On this line, we propose a new way of looking at PSVFs, by the construction of a metric space of all possible trajectories, we use it to define topological entropy of a PSVF; prove the existence of PSVFs of positive (finite and infinite) entropy and give a sufficient condition for a PSVF to have infinite topological entropy. Moreover, from this metric space, we propose a way of conjugating the dynamics of PSVFs and shift spaces. (AU) | |
| 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) |