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arXiv · 2501.03417

On the periodic orbits of C0-typical impulsive semiflows

Mario Bessa·Jaqueline Siqueira·Maria Joana Torres·Paulo Varandas
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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.

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Mario Bessa, Jaqueline Siqueira, Maria Joana Torres, Paulo Varandas. 2025-01-06. On the periodic orbits of C0-typical impulsive semiflows. https://arxiv.org/abs/2501.03417

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