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This article is cited in 1 scientific paper (total in 1 paper)
Alexey Borisov Memorial Volume
Escape Times Across the Golden Cantorus
of the Standard Map
Narcís Miguela, Carles Simóa, Arturo Vieiroab a Departament de Matemàtiques i Informàtica, Universitat de Barcelona (UB),
Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
b Centre de Recerca Matemàtica,
Campus Bellaterra, 08193 Bellaterra, Spain
Abstract:
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
$\left<N_k\right>$ to cross the Cantorus as $k\to k_G$ and showed that there
exists $B<0$ so that $\left<N_k\right>(k-k_G)^B$ 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.
Received: 29.10.2021 Accepted: 19.04.2022
Citation:
Narcís Miguel, Carles Simó, Arturo Vieiro, “Escape Times Across the Golden Cantorus
of the Standard Map”, Regul. Chaotic Dyn., 27:3 (2022), 281–306
Linking options:
https://www.mathnet.ru/eng/rcd1165 https://www.mathnet.ru/eng/rcd/v27/i3/p281
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Abstract page: | 57 | References: | 15 |
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