On the dynamics of non-autonomous systems in a~neighborhood of a~homoclinic trajectory
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915141892702208 |
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| author | Calamai, Alessandro Franca, Matteo Pospisil, Michal |
| author_facet | Calamai, Alessandro Franca, Matteo Pospisil, Michal |
| contents | This article is devoted to the study of a $2$-dimensional piecewise smooth (but possibly) discontinuous dynamical system, subject to a non-autonomous perturbation; we assume that the unperturbed system admits a homoclinic trajectory $\vecγ(t)$. Our aim is to analyze the dynamics in a neighborhood of $\vecγ(t)$ as the perturbation is turned on, by defining a Poincaré map and evaluating fly time and space displacement of trajectories performing a loop close to $\vecγ(t)$.
Besides their intrinsic mathematical interest, these results can be thought of as a first step in the analysis of several interesting problems, such as the stability of a homoclinic trajectory of a non-autonomous ODE and a possible extension of Melnikov chaos to a discontinuous setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01181 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the dynamics of non-autonomous systems in a~neighborhood of a~homoclinic trajectory Calamai, Alessandro Franca, Matteo Pospisil, Michal Dynamical Systems 34C37, 34A36, 34D10, 37G20, 37C60 This article is devoted to the study of a $2$-dimensional piecewise smooth (but possibly) discontinuous dynamical system, subject to a non-autonomous perturbation; we assume that the unperturbed system admits a homoclinic trajectory $\vecγ(t)$. Our aim is to analyze the dynamics in a neighborhood of $\vecγ(t)$ as the perturbation is turned on, by defining a Poincaré map and evaluating fly time and space displacement of trajectories performing a loop close to $\vecγ(t)$. Besides their intrinsic mathematical interest, these results can be thought of as a first step in the analysis of several interesting problems, such as the stability of a homoclinic trajectory of a non-autonomous ODE and a possible extension of Melnikov chaos to a discontinuous setting. |
| title | On the dynamics of non-autonomous systems in a~neighborhood of a~homoclinic trajectory |
| topic | Dynamical Systems 34C37, 34A36, 34D10, 37G20, 37C60 |
| url | https://arxiv.org/abs/2411.01181 |