Escape Times Across the Golden Cantorus of the Standard Map

    2022, Volume 27, Number 3, pp.  281-306

    Author(s): Miguel N., Simó C., Vieiro A.

    We consider the Chirikov standard map for values of the parameter larger than but close to Greene's $k_G$. We investigate the dynamics near the golden Cantorus and study escape rates across it. Mackay [17, 19] described the behaviour of the mean of the number of iterates $\langle N_k \rangle$ to cross the Cantorus as $k\to k_G$ and showed that there exists $B<0$ so that $\langle N_k\rangle (k-k_G)^B$ becomes 1-periodic in a suitable logarithmic scale. The numerical explorations here give evidence of the shape of this periodic function and of the relation between the escape rates and the evolution of the stability islands close to the Cantorus.
    Keywords: standard map, diffusion through a Cantor set, escape times
    Citation: Miguel N., Simó C., Vieiro A., Escape Times Across the Golden Cantorus of the Standard Map, Regular and Chaotic Dynamics, 2022, Volume 27, Number 3, pp. 281-306

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