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arXiv · 1611.03551

Anomalous dynamics and the choice of Poincar\'e recurrence-set

Matteo Sala·Roberto Artuso·Cesar Manchein
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Abstract

We investigate the dependence of Poincar\'e 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.

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Matteo Sala, Roberto Artuso, Cesar Manchein. 2016-11-11. Anomalous dynamics and the choice of Poincar\'e recurrence-set. https://doi.org/10.1103/physreve.94.052222

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