Measure of the exponential splitting of the homoclinic tangle in four-dimensional symplectic mappings

Details Measure of the exponential splitting of the homoclinic tangle in four-dimensional symplectic mappings Measure of the exponential splitting of the homoclinic tangle in four-dimensional symplectic mappings

Jun 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cemda.104..191l&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 104, Issue 1-2, pp. 191-204

Statistics

Computation

4

Hamiltonian Systems, Separatrix Splitting, Numerical Computations, Nekhoroshev Theorem, Arnold Diffusion, Symplectic Maps

Scientific paper

Using four-dimensional symplectic maps as a model problem, we numerically compute the unstable manifolds of the hyperbolic manifolds of the phase space related to the single resonances. We measure an exponential dependence of the size of the lobes of these manifolds through many orders of magnitude of the perturbing parameter. This is an indirect numerical verification of the exponential decay of the normal form, as predicted by the Nekhoroshev theorem. The variation of the size of the lobes turns out to be correlated to the diffusion coefficient.

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