Abstract
We found critical exponents for the dynamics of an ensemble of particles described by a family of Hamiltonian mappings by using the formalism of escape rates. The mappings are described by a canonical pair of variables, say action J and angle θ and the corresponding phase spaces show a large chaotic sea surrounding periodic islands and limited by a set of invariant spanning curves. When a hole is introduced in the dynamical variable action, the histogram for the frequency of escape of particles grows rapidly until reaches a maximum and then decreases towards zero for long enough time. The survival probability of the particles as a function of time is measured and statistical investigations show it is scaling invariant with respect to γ and time for chaotic orbits along the phase space.
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de Oliveira, J.A., da Costa, D.R. & Leonel, E.D. Survival probability for chaotic particles in a set of area preserving maps. Eur. Phys. J. Spec. Top. 225, 2751–2761 (2016). https://doi.org/10.1140/epjst/e2015-50330-y
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DOI: https://doi.org/10.1140/epjst/e2015-50330-y