# 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.

Access to the full text on the Springer website |