Work

Symbolic dynamics of planar piecewise smooth vector fields

Year: 2021

Type: preprint

Abstract: Recently, the theory concerning piecewise smooth vector fields (PSVFs for short) have been undergoing important improvements. In fact, many results obtained do not have an analogous for smooth vector fields. For example, the chaoticity of planar PSVFs, which is impossible for the smooth ones. These differences are generated by the non-uniqueness of trajectory passing through a point. Inspired by the classical fact that one-dimensional discrete dynamic systems can produce chaotic behavior, we construct a conjugation between the shift map and PSVFs. By means of the results obtained and the techniques employed, a new perspective on the study of PSVFs is brought to light and, through already established results for discrete dynamic systems, we will be able to obtain results regarding PSVFs.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2112.02151

Authors: Antunes, Andre Amaral, Carvalho, Tiago

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Conselho Nacional de Desenvolvimento Científico e Tecnológico

Awards: G1083246328, G1388809268, G2312790183, G295657101, Piecewise smooth vector fields with applications in biology, G7497653597, G7944345144, Piecewise smooth vector fields: Closing Lemmas, shifts and horseshoe dynamics.

OpenAlex ID: W4200634727

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