Piecewise Smooth Dynamical Systems Regularized by Convolution
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866914271809503232 |
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| author | Buzzi, Claudio A. Panazzolo, Daniel da Silva, Paulo R. |
| author_facet | Buzzi, Claudio A. Panazzolo, Daniel da Silva, Paulo R. |
| contents | We present a general regularization procedure for piecewise smooth vector fields whose discontinuity locus is a variety of normal crossings type. We show that such regularization can be smoothed through a finite sequence of blowings-up, thereby reducing the problem to study of the dynamics of a smooth vector field in a manifold with corners. The procedure will be illustrated in the cases of piecewise smooth vector fields on $\mathbb{R}^2$ with discontinuity locus $x=0$ or $xy=0$, and on $\mathbb{R}^3$ with discontinuity locus $xyz=0$. We will see that some unexpected dynamical phenomena may arise even in the case of piecewise constant vector fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00697 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Piecewise Smooth Dynamical Systems Regularized by Convolution Buzzi, Claudio A. Panazzolo, Daniel da Silva, Paulo R. Dynamical Systems 34A36, 34D15, 34C45, 34C07, 34C23, 34C25 We present a general regularization procedure for piecewise smooth vector fields whose discontinuity locus is a variety of normal crossings type. We show that such regularization can be smoothed through a finite sequence of blowings-up, thereby reducing the problem to study of the dynamics of a smooth vector field in a manifold with corners. The procedure will be illustrated in the cases of piecewise smooth vector fields on $\mathbb{R}^2$ with discontinuity locus $x=0$ or $xy=0$, and on $\mathbb{R}^3$ with discontinuity locus $xyz=0$. We will see that some unexpected dynamical phenomena may arise even in the case of piecewise constant vector fields. |
| title | Piecewise Smooth Dynamical Systems Regularized by Convolution |
| topic | Dynamical Systems 34A36, 34D15, 34C45, 34C07, 34C23, 34C25 |
| url | https://arxiv.org/abs/2601.00697 |