$C^1$-continuation of periodic orbits from homoclinics

Chong-Qing Cheng and Min Zhou

Vol. 317 (2022), No. 1, 67–118

DOI: 10.2140/pjm.2022.317.67

Abstract

We study the continuation of periodic orbits from various compounds of homoclinics in a classical system. They make up $C^1$-smooth, normally hyperbolic invariant cylinders, with which we are able to solve the problem of double resonance in a very simple way.

Keywords

normally hyperbolic invariant cylinder, Arnold diffusion

Mathematical Subject Classification

Primary: 37J40, 37J46

Milestones

Received: 4 February 2021

Revised: 31 August 2021

Accepted: 2 October 2021

Published: 19 June 2022