| Full text | |
| Author(s): |
de Rezende, Ketty A.
;
Zigart, Murilo A. de Jesus
Total Authors: 2
|
| Document type: | Journal article |
| Source: | SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES; v. N/A, p. 15-pg., 2024-10-10. |
| Abstract | |
In this paper, we consider 3x3 matrices which represent the linear part of vector fields in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>{3}$$\end{document} that are tangent vector fields when restricted to one of the following singular subsets: a cone, a cross-cap, a double crossing or a triple crossing point (transversal intersection of two or three planes in general position, respectively). We present a dynamical classification in the spirit of the trace-determinant plane for each of these singular subsets. Moreover, we propose a slightly different type of continuation, where we study the bifurcations that occur when we consider one-parameter families of matrices that make the transition from a vector field tangent to one singular subset to another. These transitions occur naturally in vector fields tangent to closed singular two-manifolds with the aforementioned singular sets, called Gutierrez-Sotomayor surfaces. Through the analysis of these continuations we relate qualitative changes on the dynamics to the geometry of the singular subsets. (AU) | |
| FAPESP's process: | 23/03430-8 - Sufficient conditions for the realization of Lyapunov graphs as Gutierrez-Sotomayor flows |
| Grantee: | Murilo André de Jesus Zigart |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |