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Study of chaos in hamiltonian systems via convergent normal forms

Werner M. Vieira·Alfredo M. O. de Almeida
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Abstract

We use Moser's normal forms to study chaotic motion in two-degree hamiltonian systems near a saddle point. Besides being convergent, they provide a suitable description of the cylindrical topology of the chaotic flow in that vicinity. Both aspects combined allowed a precise computation of the homoclinic interaction of stable and unstable manifolds in the full phase space, rather than just the Poincaré section. The formalism was applied to the Hénon-Heiles hamiltonian, producing strong evidence that the region of convergence of these normal forms extends over that originally established by Moser.

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Werner M. Vieira, Alfredo M. O. de Almeida. 1996-06-07. Study of chaos in hamiltonian systems via convergent normal forms. https://doi.org/10.1016/0167-2789(95)00233-2

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