Survival probability for chaotic particles in a set of area preserving maps

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.