title: Anomalous dynamics and the choice of Poincaré recurrence set.
abstract: We investigate the dependence of Poincaré recurrence-time statistics on the choice of recurrence set by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct relation between the shape of a recurrence set and the values of its return probability distribution in arbitrary phase-space dimensions. Such a procedure, which is shown to be quite effective in the detection of tiny regions of regular motion, allows us to explain why similar recurrence sets have very different distributions and how to modify them in order to enhance their return probabilities. Applied to data, this enables us to understand the coexistence of extremely long, transient powerlike decays whose anomalous exponent depends on the chosen recurrence set.
authors.affiliation: Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil.
authors.forename: Matteo
authors.initials: M
authors.lastname: Sala
authors.affiliation: Center for Nonlinear and Complex Systems and Dipartimento di Scienza ed Alta Tecnologia, Via Valleggio 11, 22100 Como, Italy.|INFN, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy.
authors.forename: Roberto
authors.initials: R
authors.lastname: Artuso
authors.affiliation: Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil.
authors.forename: Cesar
authors.initials: C
authors.lastname: Manchein