Chaos in Piecewise Smooth Vector Fields on Two Dimensional Torus and Sphere

TL;DR

This paper investigates the complex global dynamics, bifurcations, and chaos in piecewise smooth vector fields on two-dimensional torus and sphere, providing conditions for periodicity and density of trajectories.

Contribution

It offers new conditions for chaos, bifurcations, and minimal sets in piecewise smooth vector fields on torus and sphere, advancing understanding of their global behavior.

Findings

Conditions for periodic and dense trajectories identified

Global bifurcations characterized

Chaotic behavior of the systems described

Abstract

In this paper we study the global dynamics of piecewise smooth vector fields defined in the two dimensional torus and sphere. We provide conditions under these families exhibits periodic and dense trajectories and we describe some global bifurcations. We also study its minimal sets and characterize the chaotic behavior of the piecewise smooth vector fields defined in torus and sphere.