Abundance of periodic orbits for typical impulsive flows
Abstract
Impulsive dynamical systems, modeled by a continuous semiflow and an impulse function, may be discontinuous and may have non-intuitive topological properties, as the non-invariance of the non-wandering set or the non-existence of invariant probability measures. In this paper we study dynamical features of impulsive flows parameterized by the space of impulses. We prove that impulsive semiflows determined by a C1-Baire generic impulse are such that the set of hyperbolic periodic orbits is dense in the set of non-wandering points which meet the impulsive region. As a consequence, we provide sufficient conditions for the non-wandering set of a typical impulsive semiflow (except the discontinuity set) to be invariant. Several applications are given concerning impulsive semiflows obtained from billiard, Anosov and geometric Lorenz flows.
Keywords
Cite
@article{arxiv.2405.04667,
title = {Abundance of periodic orbits for typical impulsive flows},
author = {Jaqueline Siqueira and Maria Joana Torres and Paulo Varandas},
journal= {arXiv preprint arXiv:2405.04667},
year = {2024}
}