GSD Seminar 2023/1

Seminar 4

May 16, 2023

Speaker: Tiago de Carvalho - FFCLRP/USP

Title: Entropy for Non-Smooth Vector Fields

Abstract: Non-smooth vector fields does not have necessarily the property of uniqueness of solution passing through a point and this is responsible to enrich the behavior of the system. Even on the plane non-smooth vector fields can be chaotic, a feature impossible for the smooth or continuous case. In this work we set the ground for one to begin the study of entropy for non-smooth vector fields. We construct a metric space of all possible trajectories of a non-smooth vector field, where we define a flow inherited by the vector field and then define the topological entropy in this scenario. As a consequence, we are able to obtain some general results of this theory and give some examples of planar non-smooth vector fields with positive (finite and infinite) entropy.

10:00 GMT-3

Auditório IME/UFG

Virtual Room: meet.google.com/fvg-pmit-xud