GSD Seminar 2023/2

Seminar 14

January 30, 2024

Speaker: Me. Luan Lima da Silva - IME/UFG

Title: Polar Blow-Up Applied to Regularized Planar Filippov's Fields

Auditório do IME / 11:00 GMT-3

Abstract: The aim of the seminar is to present how the change of semi-cylindrical coordinates can be applied to the study of the dynamics of regularized Filippov’s fields. Under certain hypotheses, we can show how the change of coordinates produces a fast-slow vector field and then apply Fenichel’s theory to obtain information about the dynamics of the regularized Filippov’s field. One of the highlights of this method is to show how the results of the dynamics can be independent of the choice of transition function. The essence of this study is similar to the Blow-up method applied to the analysis of the dynamics of non-hyperbolic equilibrium points for planar polynomial fields.