| Texto completo | |
| Autor(es): |
Florentino, Marco
;
Carvalho, Tiago
;
Cassiano, Jeferson
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Dynamics and Differential Equations; v. N/A, p. 23-pg., 2025-06-16. |
| Resumo | |
In this paper we study some aspects of thermodynamic formalism, more specifically topological pressure and, as a consequence, topological entropy for piecewise smooth vector fields, using topological conjugation with shift maps and the Perron-Frobenius Operator. Some relationships between entropy and Hausdorff dimensions are also investigated. As consequences of our results, we obtain planar piecewise smooth vector fields with topological entropy and Hausdorff dimension equal to log alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log \alpha $$\end{document} for all alpha is an element of(1,2]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \in (1, 2]$$\end{document}. We stress that, for the best of our knowledge, it is the first time in the literature where the topological pressure and the Hausdorff dimension of a piecewise smooth vector field is obtained. Moreover, the obtainment of topological entropy given equal to a real number log alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log \alpha $$\end{document}, for all alpha is an element of(1,2]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \in (1, 2]$$\end{document}, is an extension of previous results where the topological entropy of the planar piecewise smooth vector fields considered are logk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log k$$\end{document}, for k a positive integer. (AU) | |
| Processo FAPESP: | 21/12395-6 - Campos vetoriais suaves por partes: aspectos teóricos e aplicações |
| Beneficiário: | Tiago de Carvalho |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II |
| Beneficiário: | Claudio Aguinaldo Buzzi |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 22/02819-6 - Sistemas dinâmicos via campos vetoriais intermitentes: aspectos teóricos e aplicações |
| Beneficiário: | Tiago de Carvalho |
| Modalidade de apoio: | Auxílio à Pesquisa - Projeto Inicial |