Periodic orbits

  1. Stability ordering of cycle expansions C. P. Dettmann and G. P. Morriss, Phys. Rev. Lett. 78, 4201-4204 (1997) pdf ps arxiv
  2. Irreversibility, diffusion and multifractal measures in thermostatted systems, C. P. Dettmann, G. P. Morriss, and L. Rondoni, Chaos, Solitons and Fractals 8, 783-792 (1997)
  3. Recent results for the thermostatted Lorentz gas, G. P. Morriss, C. P. Dettmann and L. Rondoni, Physica A 240, 84-95 (1997)
  4. Cycle expansions for intermittent diffusion C. P. Dettmann and P. Cvitanovic', Phys. Rev. E 56, 6687-6692 (1997) pdf ps arxiv
  5. 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
  6. Trace formulas for stochastic evolution operators: Weak noise perturbation theory P. Cvitanovic', C. P. Dettmann, R. Mainieri, and G. Vattay, J. Stat. Phys. 93, 981-999 (1998) ps.gz (1.2M when uncompressed) arxiv
  7. Traces and determinants of strongly stochastic operators C. P. Dettmann, Phys. Rev. E 59, 5231-5234 (1999) pdf ps html arxiv
  8. Trace formulas for stochastic evolution operators: Smooth conjugation method P. Cvitanovic', C. P. Dettmann, R. Mainieri, and G. Vattay, Nonlinearity 12, 939-953 (1999) ps arxiv
  9. Spectrum of stochastic evolution operators: Local matrix representation approach P. Cvitanovic', N. Sondergaard, G. Palla, G. Vattay, and C. P. Dettmann, Phys. Rev. E 60, 3936-3941 (1999) pdf ps Two distinct arxiv versions:arxiv arxiv
  10. Microscopic chaos and diffusion C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys. 101, 775-817 (2000) ps.gz (28 pages; 2.1M when uncompressed) arxiv
  11. Noise corrections to stochastic trace formulas G. Palla, G. Vattay, A. Voros, N. Sondergaard, C. P. Dettmann, Found. Phys. 31, 641-657 (2001). arxiv
  12. Stable synchronised states of coupled Tchebyscheff maps, C. P. Dettmann, Physica D 172 88-102 (2002). ps.gz(1.3M when uncompressed) animation (0.3M) arxiv
  13. Lyapunov spectra of periodic orbits for a many-particle system, T. Taniguchi, C. P. Dettmann and G. P. Morriss, J. Stat. Phys. 109 747-764 (2002). pdf ps.gz(1.0M when uncompressed). arxiv
  14. Fractal asymptotics, C. P. Dettmann, Physica D 187, 214-222 (2004). ps arxiv
  15. 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
  16. 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
  17. Dependence of chaotic diffusion on the size and position of holes, G. Knight, O. Georgiou, C. P. Dettmann, R. Klages, Chaos 22 023132 (2012). pdf arxiv
  18. Ergodicity of a single particle confined in a nanopore, S. Bernardi, J. S. Hansen, F. Frascoli, B. D. Todd and C. P. Dettmann, J. Stat. Phys. 148 1156-1169 (2012). pdf
  19. Faster than expected escape for a class of fully chaotic maps, O. Georgiou, C. P. Dettmann, E. G. Altmann, Chaos 22 043115 (2012). arxiv pdf
  20. Open circle maps: Small hole asymptotics, C. P. Dettmann, Nonlinearity 26 307-317 (2013). pdf arxiv
  21. Escape through a time-dependent hole in the doubling map, A. L. P. Livorati, O. Georgiou, C. P. Dettmann and E. D. Leonel, Phys. Rev. E, 89 052913 (2014). arxiv pdf
  22. Survival probability for open spherical billiards, C. P. Dettmann and M. R. Rahman, Chaos 24 043130 (2014). arxiv pdf
  23. Circular, elliptic and oval billiards in a gravitational field, D. R. Costa, C. P. Dettmann and E. D. Leonel, Commun. Nonlin. Sci. Numer. Sim., 22 731-746 (2015). pdf
  24. Linear and nonlinear stability of periodic orbits in annular billiards, C. P. Dettmann and V. Fain, Chaos 27 043106 (2017). arxiv.
  25. A billiard in an open circle and the Riemann zeta function L. A. Bunimovich and C. P. Dettmann, Exper. Math. (published online). pdf.
  26. Book chapter: The Lorentz gas as a paradigm for nonequilibrium stationary states, C. P. Dettmann, pp 315-365 in Hard ball systems and the Lorentz gas (edited by D. Szasz), Encyclopaedia of Mathematical Sciences Vol 101 (Springer, 2000). Full size version, 50 pages pdf. Environmental microscopic version, 25 pages pdf.
  27. Web book contribution: "Stability ordering of cycle expansions" in the chapter "cycle expansions" in Classical and Quantum Chaos webbook, P. Cvitanovic' et al chaosbook.org
  28. Poster: Recent developments in periodic orbit theory C. P. Dettmann April 2002. ps

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