Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems
Abstract

The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study this problem in the followinga prioriunstable Hamiltonian system with a time-periodic perturbation$Hε(p,q,I,φ,t)=h(I)+∑i=1n±12pi2+Vi(qi)+εH1(p,q,I,φ,t),$where$(p,q)∈Rn×Tn$,$(I,φ)∈Rd×Td$withn,d⩾ 1,Viare Morse potentials, andɛis a small non-zero parameter. The unperturbed Hamiltonian is not necessarily convex, and the induced inner dynamics does not need to satisfy a twist condition. Using geometric methods we prove that Arnold diffusion occurs for generic analytic perturbationsH1. Indeed, the set of admissibleH1isCωdense andC3open (a fortiori,Cωopen). Our perturbative technique for the genericity is valid in theCktopology for allk∈ [3, ∞) ∪ {∞,ω}.

Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10363698
Journal Name:
Nonlinearity
Volume:
35
Issue:
4
Page Range or eLocation-ID:
p. 1986-2019
ISSN:
0951-7715
Publisher:
IOP Publishing
National Science Foundation
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