Vol. 317, No. 1, 2022

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

Chong-Qing Cheng and Min Zhou

Vol. 317 (2022), No. 1, 67–118
Abstract

We study the continuation of periodic orbits from various compounds of homoclinics in a classical system. They make up C1-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
Authors
Chong-Qing Cheng
Department of Mathematics
Nanjing University
Nanjing
China
Min Zhou
Department of Mathematics
Nanjing University
Nanjing
China