Markov tree model of transport in area-preserving maps. (English) Zbl 0658.60144
Transport in an area-preserving map with a mixture of regular and chaotic regions is described in terms of the flux through invariant Cantor sets called cantori. A model retaining a discrete set of cantori approaching a boundary circle gives the Markov chain description of J. D. Hanson, J. R. Cary and the first author [J. Stat. Phys. 39, 327 ff. (1985)]. The inclusion of cantori surrounding island chains, and islands about islands, etc. gives a Markov tree model with a slower decay rate. The survival probability distribution is shown to decay asymptotically as a power law. The decay exponent agrees reasonably well with the computations of C. F. F. Karney [Physica D 8, 360-380 (1983)] and of B. V. Chirikov and D. L. Shepelyanski [ibid. 13, 395-400 (1984; Zbl 0588.58039)].
MSC:
| 60K99 | Special processes |
| 81P20 | Stochastic mechanics (including stochastic electrodynamics) |
| 58C99 | Calculus on manifolds; nonlinear operators |
Keywords:
area-preserving map; regular and chaotic regions; survival probability distribution; decay exponentCitations:
Zbl 0588.58039References:
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