On the periodic orbits of C0-typical impulsive semiflows
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915901886955520 |
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| author | Bessa, Mario Siqueira, Jaqueline Torres, Maria Joana Varandas, Paulo |
| author_facet | Bessa, Mario Siqueira, Jaqueline Torres, Maria Joana Varandas, Paulo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the periodic orbits of C0-typical impulsive semiflows Bessa, Mario Siqueira, Jaqueline Torres, Maria Joana Varandas, Paulo Dynamical Systems 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. |
| title | On the periodic orbits of C0-typical impulsive semiflows |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2501.03417 |