Year: 2019
Type: article
Abstract: In this paper, we introduce the concept of sliding Shilnikov orbits for 3D Filippov systems. In short, such an orbit is a piecewise smooth closed curve, composed by Filippov trajectories, which slides on the switching surface and connects a Filippov equilibrium to itself, namely, a pseudo-saddle-focus. A version of Shilnikov's theorem is provided for such systems. Particularly, we show that sliding Shilnikov orbits occur in generic one-parameter families of Filippov systems and that arbitrarily close to a sliding Shilnikov orbit there exist countably infinitely many sliding periodic orbits. Here, no additional Shilnikov-like assumption is needed in order to get this last result. In addition, we show the existence of sliding Shilnikov orbits in discontinuous piecewise linear differential systems. As far as we know, the examples of Fillippov systems provided in this paper are the first to exhibit such a sliding phenomenon.
DOI: 10.1063/1.5093067
Authors: Douglas D. Novaes, Marco A. Teixeira
Institution: Universidade Estadual de Campinas (UNICAMP)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1772140372