Escape Times Across the Golden Cantorus of the Standard Map

Abstract

We consider the Chirikov standard map for values of the parameterlarger than but close to Greene’s kG. We investigate the dynamics near thegolden Cantorus and study escape rates across it.Mackay [17, 19]described the behaviour of the mean of the number of iterates (Formula presented.) to cross the Cantorus as (Formula presented.) and showed that thereexists B<0 so that (Formula presented.) becomes 1-periodic in asuitable logarithmic scale. The numerical explorations here give evidence ofthe shape of this periodic function and of the relation between the escaperates and the evolution of the stability islands close to the Cantorus. © 2022, Pleiades Publishing, Ltd.