The Orbit Space Approach for Piecewise Smooth Vector Fields
Dynamical Systems
2025-10-07 v2
Abstract
In this work we develop a well-defined theory of orbit spaces for piecewise smooth vector fields (PSVFs). This approach is inspired by the techniques already used in the study of endomorphisms, namely inverse limit analysis, and has been used before for PSVFs. We then apply the construction of our theory to understanding transitivity in PSVFs. Our results prove that the known examples of transitive PSVFs in the literature, the bean model and the sphere model, are indeed transitive in the orbit space.
Cite
@article{arxiv.2310.13804,
title = {The Orbit Space Approach for Piecewise Smooth Vector Fields},
author = {Otávio M. L. Gomide and Pedro G. Mattos and Régis Varão},
journal= {arXiv preprint arXiv:2310.13804},
year = {2025}
}