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Statistical and dynamical properties of a dissipative kicked rotator

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  • Oliveira, Diego F.M.
  • Leonel, Edson D.

Abstract

Some dynamical and statistical properties for a conservative as well as the dissipative problem of relativistic particles in a waveguide are considered. For the first time, two different types of dissipation namely: (i) due to viscosity and; (ii) due to inelastic collision (upon the kick) are considered individually and acting together. For the first case, and contrary to what is expected for the original Zaslavsky’s relativistic model, we show there is a critical parameter where a transition from local to global chaos occurs. On the other hand, after considering the introduction of dissipation also on the kick, the structure of the phase space changes in the sense that chaotic and periodic attractors appear. We study also the chaotic sea by using scaling arguments and we proposed an analytical argument to reinforce the validity of the scaling exponents obtained numerically. In principle such an approach can be extended to any two-dimensional map. Finally, based on the Lyapunov exponent, we show that the parameter space exhibits infinite families of self-similar shrimp-shape structures, corresponding to periodic attractors, embedded in a large region corresponding to chaotic attractors.

Suggested Citation

  • Oliveira, Diego F.M. & Leonel, Edson D., 2014. "Statistical and dynamical properties of a dissipative kicked rotator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 498-514.
    • Handle: RePEc:eee:phsmap:v:413:y:2014:i:c:p:498-514
    DOI: 10.1016/j.physa.2014.06.005
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    References listed on IDEAS

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    1. Oliveira, Diego F.M. & Leonel, Edson D., 2010. "Suppressing Fermi acceleration in a two-dimensional non-integrable time-dependent oval-shaped billiard with inelastic collisions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1009-1020.
    2. Gallas, Jason A.C., 1994. "Dissecting shrimps: results for some one-dimensional physical models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(1), pages 196-223.
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