Cambridge Journal of Mathematics

Volume 5 (2017)

Number 2

Dynamics around the double resonance

Pages: 153 – 228



Chong-Qing Cheng (Department of Mathematics, Nanjing University, Nanjing, China)


In this paper, we study time-periodic perturbation of classical systems with two degrees of freedom. A transition chain is established, by passing through small neighborhood of double resonant point, to connect any two cohomology classes corresponding to resonant frequencies. Applying the result to nearly integrable Hamiltonian systems with three degrees of freedom, one obtains a transition chain along which one is able to construct diffusion orbits suggested by V. I. Arnold in [A66].

2010 Mathematics Subject Classification

Primary 37J40, 37J50. Secondary 49L25.

Published 16 May 2017