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arXiv · 2405.04667

Abundance of periodic orbits for typical impulsive flows

Jaqueline Siqueira·Maria Joana Torres·Paulo Varandas
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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.

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Jaqueline Siqueira, Maria Joana Torres, Paulo Varandas. 2024-05-07. Abundance of periodic orbits for typical impulsive flows. https://arxiv.org/abs/2405.04667

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