Journal of Statistical Physics

, Volume 39, Issue 3, pp 327–345

Algebraic decay in self-similar Markov chains

  • James D. Hanson
  • John R. Cary
  • James D. Meiss
Articles

DOI: 10.1007/BF01018666

Cite this article as:
Hanson, J.D., Cary, J.R. & Meiss, J.D. J Stat Phys (1985) 39: 327. doi:10.1007/BF01018666

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.

Key words

Birth and death processHamiltonianstochasticity

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • James D. Hanson
    • 1
  • John R. Cary
    • 1
  • James D. Meiss
    • 1
  1. 1.Institute for Fusion StudiesThe University of Texas at AustinAustin
  2. 2.Department of PhysicsAuburn UniversityAuburn
  3. 3.Department of Astrophysical, Planetary, and Atmospheric SciencesUniversity of ColoradoBoulder