Asymptotic trajectories of KAM torus

2013/12/07 by Zhang, Jianlu, Cheng, Chong-Qing
#37Dxx #37JXX #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1312.2102

Abstract

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), (q,p)∈ T^*\mathbbT²,t∈ \mathbbS¹=ℝ/ℤ, with a self-similar and weak-coupled f(p,q,t) and h(p) strictly convex. For a given Diophantine rotation vector ω, we can find asymptotic orbits towards the KAM torus T_ω, which persists owing to the classical KAM theory, as long as ε≪1 sufficiently small and f∈ C^r(T^*\mathbbT²×\mathbbS¹,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.

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