Chaos induced by sliding phenomena in Filippov systems

TL;DR

This paper analyzes the complex chaotic dynamics near a sliding Shilnikov orbit in Filippov systems, showing the first return map exhibits Bernoulli shift behavior with infinite entropy and many periodic points.

Contribution

It provides a complete topological and ergodic characterization of chaos near sliding Shilnikov orbits in Filippov systems, including conjugacy to Bernoulli shifts.

Findings

First return map is conjugate to a Bernoulli shift

Infinite topological entropy in the system

Existence of infinitely many periodic points for each period

Abstract

In this paper we provide a full topological and ergodic description of the dynamics of Filippov systems nearby a sliding Shilnikov orbit. More specifically we prove that the first return map, defined nearby this orbit, is topologically conjugate to a Bernoulli shift with infinite topological entropy. In particular, we see that for each natural number m it has infinitely many periodic points with period m.