2024/05/07 by Jaqueline Siqueira, Siqueira, Jaqueline, Maria Joana Torres +3
Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2405.04667
openalex publication_date 2024/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.