Dynamics around the double resonance

Chongqing Cheng Nanjing University

Dynamical Systems mathscidoc:1705.11001

Cambridge J. Mathematics, 5, (2), 153-228, 2017
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 Arnold in [A66].
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  title={Dynamics around the double resonance},
  author={Chongqing Cheng},
  booktitle={Cambridge J. Mathematics},
Chongqing Cheng. Dynamics around the double resonance. 2017. Vol. 5. In Cambridge J. Mathematics. pp.153-228. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170530165644584057776.
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