Asymptotic trajectories of KAM torus
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2013
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| _version_ | 1866911244267552768 |
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| author | Zhang, Jianlu Cheng, Chong-Qing |
| author_facet | Zhang, Jianlu Cheng, Chong-Qing |
| contents | In this paper we construct a certain type of nearly integrable systems of two and a half degrees of freedom:
\[H(p,q,t)=h(p)+εf(p,q,t),\quad (q,p)\in T^{*}\mathbb{T}^2,t\in \mathbb{S}^1=\mathbb{R}/\mathbb{Z},
\] with a self-similar and weak-coupled $f(p,q,t)$ and $h(p)$ strictly convex. For a given Diophantine rotation vector $\vecω$, we can find asymptotic orbits towards the KAM torus $\mathcal{T}_ω$, which persists owing to the classical KAM theory, as long as $ε\ll1$ sufficiently small and $f\in C^r(T^{*}\mathbb{T}^2\times\mathbb{S}^1,\mathbb{R})$ properly smooth. The construction bases on the new methods developed in {\it a priori} stable Arnold Diffusion problem by Chong-Qing Cheng. As an expansion of that, this paper sheds some light on the seeking of much preciser diffusion orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1312_2102 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Asymptotic trajectories of KAM torus Zhang, Jianlu Cheng, Chong-Qing Dynamical Systems 37JXX, 37Dxx In this paper we construct a certain type of nearly integrable systems of two and a half degrees of freedom: \[H(p,q,t)=h(p)+εf(p,q,t),\quad (q,p)\in T^{*}\mathbb{T}^2,t\in \mathbb{S}^1=\mathbb{R}/\mathbb{Z}, \] with a self-similar and weak-coupled $f(p,q,t)$ and $h(p)$ strictly convex. For a given Diophantine rotation vector $\vecω$, we can find asymptotic orbits towards the KAM torus $\mathcal{T}_ω$, which persists owing to the classical KAM theory, as long as $ε\ll1$ sufficiently small and $f\in C^r(T^{*}\mathbb{T}^2\times\mathbb{S}^1,\mathbb{R})$ properly smooth. The construction bases on the new methods developed in {\it a priori} stable Arnold Diffusion problem by Chong-Qing Cheng. As an expansion of that, this paper sheds some light on the seeking of much preciser diffusion orbits. |
| title | Asymptotic trajectories of KAM torus |
| topic | Dynamical Systems 37JXX, 37Dxx |
| url | https://arxiv.org/abs/1312.2102 |