Tunable Orbits Influence in a Driven Stadium-Like Billiard

  • André L. P. LivoratiEmail author
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 22)


The dynamics of a driven stadium-like billiard is investigated through a four-dimensional nonlinear mapping. We set a critical resonance velocity, which plays the role of an ensemble separation according to the initial velocities. When the resonance is active, the invariant curves that surround the stability islands become stochastic layers, thus allowing a change in the dynamics from chaos to stability and vice versa, leading the root mean square velocity to steady state plateaus for long times. A tunneling behavior of orbits in the lower ensemble was characterized via transport analysis and Lyapunov exponents. Our results may be extended to other similar dynamical systems that may present similar critical resonances.



ALPL acknowledges FAPESP (2014/25316-3) and FAPESP (2015/26699-6) for financial support. ALPL also thanks the University of Bristol for the kind hospitality during his stay in UK. This research was supported by resources supplied by the Center for Scientific Computing (NCC/GridUNESP) of the São Paulo State University (UNESP). The author also acknowledges Alexander Loskutov (in memorian) for the art of Fig. 4.1.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de FísicaUNESP - Univ Estadual PaulistaRio ClaroBrazil
  2. 2.School of MathematicsUniversity of BristolBristolUK

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