## Abstract

We consider a family of two-dimensional nonlinear area-preserving mappings that generalize the Chirikov standard map and model a variety of periodically forced systems. The action variable diffuses in increments whose phase is controlled by a negative power of the action and hence effectively uncorrelated for small actions, leading to a chaotic sea in phase space. For larger values of the action the phase space is mixed and contains a family of elliptic islands centered on periodic orbits and invariant Kolmogorov-Arnold-Moser (KAM) curves. The transport of particles along the phase space is considered by starting an ensemble of particles with a very low action and letting them evolve in the phase until they reach a certain height h. For chaotic orbits below the periodic islands, the survival probability for the particles to reach h is characterized by an exponential function, well modeled by the solution of the diffusion equation. On the other hand, when h reaches the position of periodic islands, the diffusion slows markedly. We show that the diffusion coefficient is scaling invariant with respect to the control parameter of the mapping when h reaches the position of the lowest KAM island.

Original language | English |
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Article number | 062904 |

Number of pages | 5 |

Journal | Physical Review E: Statistical, Nonlinear, and Soft Matter Physics |

Volume | 87 |

Issue number | 6 |

DOIs | |

Publication status | Published - 10 Jun 2013 |

## Keywords

- ANOMALOUS TRANSPORT
- CHAOTIC SYSTEMS
- ESCAPE RATES
- TIME