Cambridge Journal of Mathematics
Volume 5 (2017)
Dynamics around the double resonance
Pages: 153 – 228
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.