On Shilnikov's scenario with a homoclinic orbit in 3D
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913670414467072 |
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| author | Walther, Hans-Otto |
| author_facet | Walther, Hans-Otto |
| contents | The paper provides a detailed proof that complicated motion exists in Shilnikov's scenario of a smooth vectorfield $V$ on $mathbb{R}^3$ with $V(0)=0$ so that the equation $x'=V(x)$ has a homoclinic solution $h$ with $\lim_{|t|\to\infty}h(t)=0$, and $DV(0)$ has eigenvalues $u>0$ and $σ\pmμ$, $σ<0<μ$, with $0<σ+u$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18289 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Shilnikov's scenario with a homoclinic orbit in 3D Walther, Hans-Otto Dynamical Systems Classical Analysis and ODEs 37D45, 34C28 The paper provides a detailed proof that complicated motion exists in Shilnikov's scenario of a smooth vectorfield $V$ on $mathbb{R}^3$ with $V(0)=0$ so that the equation $x'=V(x)$ has a homoclinic solution $h$ with $\lim_{|t|\to\infty}h(t)=0$, and $DV(0)$ has eigenvalues $u>0$ and $σ\pmμ$, $σ<0<μ$, with $0<σ+u$. |
| title | On Shilnikov's scenario with a homoclinic orbit in 3D |
| topic | Dynamical Systems Classical Analysis and ODEs 37D45, 34C28 |
| url | https://arxiv.org/abs/2406.18289 |