Year: 2022
Type: article
Abstract: The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study this problem in the following a priori unstable Hamiltonian system with a time-periodic perturbation H ε ( p , q , I , φ , t ) = h ( I ) + ∑ i = 1 n ± 1 2 p i 2 + V i ( q i ) + ε H 1 ( p , q , I , φ , t ) , where ( p , q ) ∈ R n × T n , ( I , φ ) ∈ R d × T d with n, d ⩾ 1, V i are Morse potentials, and ɛ is 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 perturbations H 1. In
Source: Nonlinearity
Authors: Qinbo Chen, Rafael de la Llave
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,930
Award: G722836977
OpenAlex ID: W3134787524