https://doi.org/10.1140/epjst/e2015-50330-y
Regular Article
Survival probability for chaotic particles in a set of area preserving maps
1 UNESP, University Estadual Paulista, Câmpus de São João da Boa Vista, Av. Professora Isette Corrêa Fontão, 505, Jardim Santa Rita das Areias, 13876-750, São João da Boa Vista, SP, Brazil
2 Departamento de Física, UNESP, University Estadual Paulista, Av.24A, 1515, Bela Vista, 13506-900, Rio Claro, SP, Brazil
3 Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
a e-mail: julianoantonio@sjbv.unesp.br
Received: 21 December 2015
Revised: 25 February 2016
Published online: 22 November 2016
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.
© EDP Sciences, Springer-Verlag, 2016
