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arXiv · 2406.18289

On Shilnikov's scenario with a homoclinic orbit in 3D

Hans-Otto Walther
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Abstract

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 $\sigma\pm\mu$, $\sigma<0<\mu$, with $0<\sigma+u$.

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Hans-Otto Walther. 2024-06-26. On Shilnikov's scenario with a homoclinic orbit in 3D. https://arxiv.org/abs/2406.18289

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