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We investigate the dependence of Poincar\'e recurrence-times statistics onthe choice of recurrence-set, by sampling the dynamics of two- andfour-dimensional Hamiltonian maps. We derive a method that allows us tovisualize the direct relation between the shape of a recurrence-set and thevalues of its return probability distribution in arbitrary phase-spacedimensions. Such procedure, which is shown to be quite effective in thedetection of tiny regions of regular motion, allows to explain it why similarrecurrence-sets have very different distributions and how to modify them inorder to enhance their return probabilities. Applied on data, this permits tounderstand the co-existence of extremely long, transient power-like decayswhose anomalous exponent depends on the chosen recurrence-set.

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