Abstract
Numerical experiments on a symplectic coupled map system are performed to investigate the tendency for global ergodic behavior of typical Hamiltonian systems as the number of degrees of freedom N is increased. As N increases, we find that the fraction of phase space volume occupied by invariant tori decreases strongly. Nevertheless, due to observed very long time correlated behavior, a conclusion of effective gross ergodicity cannot be confirmed, even though extremely long numerical runs were employed.
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References
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We had completed our research at the time of the publication of the paper of Falcioni et al. Because of the similarity of that work and ours, in this Letter we shall be somewhat briefer than we otherwise might have been, and will also emphasize that part of our work which is different from that of Falcioni et al.
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Hurd, L., Grebogi, C., Ott, E. (1994). On the Tendency Toward Ergodicity with Increasing Number of Degrees of Freedom in Hamiltonian Systems. In: Seimenis, J. (eds) Hamiltonian Mechanics. NATO ASI Series, vol 331. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0964-0_9
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DOI: https://doi.org/10.1007/978-1-4899-0964-0_9
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