Intermittent dynamics

    Intermittency is the general dynamical phonemenon in which the dynamics switches, apparently randomly, between regular and chaotic behaviour. This work is concerned with the computation of the properties of intermittent systems using periodic orbits. In a nutshell, there are long but relatively stable periodic orbits that dominate the calculation, so it is important to order periodic orbit expansions by stability rather than length. A number of other techniques are also investigated in order to further accelerate convergence. Models include simple maps and the thermostatted Lorentz gas.

  1. Crisis in the periodic Lorentz gas. C. P. Dettmann and G. P. Morriss, Phys. Rev. E 54, 4782-4790 (1996) pdf (4.9M)
  2. Stability ordering of cycle expansions C. P. Dettmann and G. P. Morriss, Phys. Rev. Lett. 78, 4201-4204 (1997) pdf ps arxiv
  3. Cycle expansions for intermittent diffusion C. P. Dettmann and P. Cvitanovic', Phys. Rev. E 56, 6687-6692 (1997) pdf ps arxiv
  4. Computing the diffusion coefficient for intermittent maps: Resummation of stability ordered cycle expansions C. P. Dettmann and P. Dahlqvist, Phys. Rev. E 57, 5303-5310 (1998) pdf ps.gz arxiv
  5. Periodic orbit theory of two coupled Tchebyscheff maps, C. P. Dettmann and D. Lippolis, Chaos, Solitons and Fractals 23 43-54 (2005). ps pdf arxiv
  6. Product of n independent uniform random variables, C. P. Dettmann and O. Georgiou, Stat. Prob. Lett., 79, 2501-2503 (2009). pdf
  7. Survival probability for the stadium billiard, C. P. Dettmann and O. Georgiou, Physica D, 238, 2395-2403 (2009). pdf arxiv
  8. Transmission and reflection in the stadium billiard: Time-dependent asymmetric transport, C. P. Dettmann and O. Georgiou, Phys. Rev. E 83 036212 (2011). [Selected to appear in the PRE "Kaleidoscope"] pdf arxiv poster
  9. Open mushrooms: Stickiness revisited, C. P. Dettmann and O. Georgiou, J. Phys. A.: Math. Theor. 44 195102 (2011). [Highlighted in a JPA Insights article.] pdf arxiv poster
  10. New horizons in multidimensional diffusion: The Lorentz gas and the Riemann Hypothesis, C. P. Dettmann, J. Stat. Phys. 146 181-204 (2012). pdf arxiv animation (4.8M)
  11. Quantifying intermittency in the open drivebelt billiard, C. P. Dettmann and O. Georgiou, Chaos 22 026113 (2012). pdf arxiv
  12. Keyhole and Reflection Effects in Network Connectivity Analysis, M. Z. Bocus, C. P. Dettmann, J. P. Coon, M. R. Rahman, submitted arxiv.
  13. Periodic volume fluctuations with infinite horizon: Intermittency enhanced Fermi acceleration, C. P. Dettmann and E. D. Leonel, submitted pdf
  14. Web book contribution: "Stability ordering of cycle expansions" (currently section 20.5) in Classical and Quantum Chaos webbook, P. Cvitanovic' et al html

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