Algebraic decay in self-similar Markov chains View Full Text


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Article Info

DATE

1985-05

AUTHORS

James D. Hanson, John R. Cary, James D. Meiss

ABSTRACT

A continuous-time Markov chain is used to model motion in the neighborhood of a critical invariant circle for a Hamiltonian map. States in the infinite chain represent successive rational approximants to the frequency of the invariant circle. For the case of a noble frequency, the chain is self-similar and the nonlinear integral equation for the first passage time distribution is solved exactly. The asymptotic distribution is a power law times a function periodic in the logarithm of the time. For parameters relevant to the critical noble circle, the decay proceeds ast−4.05. More... »

PAGES

327-345

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01018666

DOI

http://dx.doi.org/10.1007/bf01018666

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1045723712


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