title: Scaling invariance of the diffusion coefficient in a family of two-dimensional Hamiltonian mappings.
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.
authors.affiliation: Departamento de Física, UNESP, Universidade Estadual Paulista, Avenida 24A, 1515 13506-900, Rio Claro, São Paulo, Brazil.
authors.forename: Juliano A
authors.initials: JA
authors.lastname: de Oliveira
authors.forename: Carl P
authors.initials: CP
authors.lastname: Dettmann
authors.forename: Diogo R
authors.initials: DR
authors.lastname: da Costa
authors.forename: Edson D
authors.initials: ED
authors.lastname: Leonel