Study of chaos in hamiltonian systems via convergent normal forms

Details Study of chaos in hamiltonian systems via convergent normal forms Study of chaos in hamiltonian systems via convergent normal forms

1996-06-07

arxiv.org/abs/chao-dyn/9606002v1

Physica D{\bf{90}}, 9 (1996)

Nonlinear Sciences

Chaotic Dynamics

29 pages, REVTEX, 22 postscript figures on request

Scientific paper

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 Poincar\'e section. The formalism was applied to the H\'enon-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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