任意自由度和常双曲不变圆柱中的Arnold扩散
Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders
摘要：
我们证明了Arnold扩散的先验稳定的情况下的一种形式。设H 0（p）+ $ε$ H 1（$θ$，p，t），$θ$ $\in$ Tn，p $\in$ Bn，t $\in$ T = R/T是一个具有严格凸H 0的任意自由度n2的近可积系统.我们证明了对于“一般的”$ε$ H1，存在一个轨道（$θ$，p）（t）满足p（t）-- p（0）{ \textgreater } l（H1）{ \textgreater } 0，其中l（H1）与$ε$无关.扩散轨道沿着余维1共振行进，并且我们构造的唯一障碍是附加共振的有限集。对于证明，我们使用的组合几何和变分方法，并设法适应工具，最近开发的先验不稳定的情况下。
英文摘要：
We prove a form of Arnold diffusion in the a priori stable case. Let H0(p) + $ε$H1($θ$, p, t), $θ$ $\in$ T n , p $\in$ B n , t $\in$ T = R/T be a nearly integrable system of arbitrary degrees of freedom n 2 with a strictly convex H0. We show that for a "generic" $ε$H1, there exists an orbit ($θ$, p)(t) satisfying p(t) -- p(0) {\textgreater} l(H1) {\textgreater} 0, where l(H1) is independent of $ε$. The diffusion orbit travels along a co-dimension one resonance , and the only obstruction to our construction is a finite set of additional resonances. For the proof we use a combination geometric and variational methods, and manage to adapt tools which have recently been developed in the a priori unstable case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
