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.
arXiv comment11 pages, 6 figures, 4 appendices, accepted on Phys. Rev. E
References in corpus (13)
- Long-Time Correlations in the Stochastic Regime
- Characterizing dynamics with covariant Lyapunov vectors
- On universality of algebraic decays in Hamiltonian systems
- Visualization and comparison of classical structures and quantum states of 4D maps
- Hypothesis of strong chaos and anomalous diffusion in coupled symplectic maps
- Hamiltonian intermittency and Lévy flights in the three-body problem
- Instability statistics and mixing rates
- Fluctuations of finite-time stability exponents in the standard map and the detection of small islands
- Characterizing Weak Chaos using Time Series of Lyapunov Exponents
- Poincaré recurrences in Hamiltonian systems with a few degrees of freedom
- Poincaré recurrences and Ulam method for the Chirikov standard map
- Recurrence-time statistics in non-Hamiltonian volume preserving maps and flows
- Algebraic statistics of Poincaré recurrences in DNA molecule