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 animation (30.5M)
  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. Periodic compression of an adiabatic gas: Intermittency enhanced Fermi acceleration, C. P. Dettmann and E. D. Leonel, EPL 103 40003 (2013). pdf
  13. Separation of particles leading to decay and unlimited growth of energy in a driven stadium-like billiard, A. L. P. Livorati, M. S. Palmero, C. P. Dettmann, I. L. Caldas, E. D. Leonel, J. Phys. A.: Math. Theor., 47 365101 (2014). arxiv
  14. Diffusion in the Lorentz gas, C. P. Dettmann, Commun. Theor. Phys. 62 521-540 (2014). pdf arxiv
  15. Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism, D. R. Costa, C. P. Dettmann, J. A. de Oliveira and E. D. Leonel, Chaos 25 033109 (2015). pdf.
  16. Network connectivity in non-convex domains with reflections, O. Georgiou, M. Z. Bocus, M. R. Rahman, C. P. Dettmann and J. P. Coon, IEEE Commun. Lett. 19 427-430 (2015). pdf arxiv.
  17. Conference paper: How sticky is the chaos/order boundary? C. P. Dettmann, Contemporary Mathematics 698 111-128 (2017). pdf arxiv.
  18. Web book contribution: "Stability ordering of cycle expansions" in the chapter "cycle expansions" in Classical and Quantum Chaos webbook, P. Cvitanovic' et al

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