Algebraic decay in self-similar Markov chains
- Cite this article as:
- Hanson, J.D., Cary, J.R. & Meiss, J.D. J Stat Phys (1985) 39: 327. doi:10.1007/BF01018666
- 66 Downloads
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.