A Piecewise Smooth $λ$-Lemma
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918091508678656 |
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| author | Buzzi, Claudio A. Santana, Paulo Silva, Luan V. M. F. |
| author_facet | Buzzi, Claudio A. Santana, Paulo Silva, Luan V. M. F. |
| contents | In this paper we provide extensions of the $λ$-Lemma (also known as Inclination Lemma) for piecewise smooth vector fields and maps. In order to achieve our main result, we investigate the regularity of time-T-maps of piecewise smooth vector fields defined at crossing orbits. We prove that these maps are homeomorphisms and also piecewise smooth diffeomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10896 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Piecewise Smooth $λ$-Lemma Buzzi, Claudio A. Santana, Paulo Silva, Luan V. M. F. Dynamical Systems 37C29, 34A36, and 34C37 In this paper we provide extensions of the $λ$-Lemma (also known as Inclination Lemma) for piecewise smooth vector fields and maps. In order to achieve our main result, we investigate the regularity of time-T-maps of piecewise smooth vector fields defined at crossing orbits. We prove that these maps are homeomorphisms and also piecewise smooth diffeomorphisms. |
| title | A Piecewise Smooth $λ$-Lemma |
| topic | Dynamical Systems 37C29, 34A36, and 34C37 |
| url | https://arxiv.org/abs/2507.10896 |