On the periodic orbits of C0-typical impulsive semiflows

TL;DR

This paper studies impulsive semiflows, showing that generically, they have dense periodic orbits on key sets, enhancing the topological understanding of these systems.

Contribution

It demonstrates that generic continuous flows and impulses produce impulsive semiflows with dense periodic orbits on their non-wandering and impulsive non-wandering sets.

Findings

Impulsive semiflows have dense periodic orbits on the non-wandering set.

Impulsive semiflows have dense periodic orbits on the impulsive non-wandering set.

Results hold for $C^0$-generic continuous flows and impulses.

Abstract

Impulsive semiflows modeled by continuous flows and continuous impulsive functions, defined over an impulsive region, are piecewise continuous semiflows with piecewise smooth trajectories. In this paper we contribute to the topological description of typical impulsive semiflows, parameterized by both flows and impulses. We prove that $C^0$-generic continuous flows generate impulsive semiflows with denseness of periodic orbits on the non-wandering set. Additionally, we show that $C^0$-generic impulses generate impulsive semiflows with denseness of periodic orbits on the impulsive non-wandering set.