Anomalous dynamics and the choice of Poincaré recurrence-set
arXiv:1611.03551 · doi:10.1103/PhysRevE.94.052222
Abstract
We investigate the dependence of Poincaré recurrence-times 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 procedure, which is shown to be quite effective in the detection of tiny regions of regular motion, allows to explain it why similar recurrence-sets have very different distributions and how to modify them in order to enhance their return probabilities. Applied on data, this permits to understand the co-existence of extremely long, transient power-like decays whose anomalous exponent depends on the chosen recurrence-set.
11 pages, 6 figures, 4 appendices, accepted on Phys. Rev. E
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