Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion

@article{Delshams2013InstabilityOH,
  title={Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion},
  author={Amadeu Delshams and Rafael de la Llave and Tere M. Seara},
  journal={Advances in Mathematics},
  year={2013},
  volume={294},
  pages={689-755}
}
Abstract We consider models given by Hamiltonians of the form H ( I , φ , p , q , t ; e ) = h ( I ) + ∑ j = 1 n ± ( 1 2 p j 2 + V j ( q j ) ) + e Q ( I , φ , p , q , t ; e ) where I ∈ I ⊂ R d , φ ∈ T d , p , q ∈ R n , t ∈ T 1 . These are higher dimensional analogues, both in the center and hyperbolic directions, of the models studied in [28] , [29] , [43] and are usually called “a-priori unstable Hamiltonian systems”. All these models present the large gap problem. We show that, for 0 e ≪ 1… Expand
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