De Oliveira, Juliano A. [UNESP]Dettmann, Carl P.Da Costa, Diogo R.Leonel, Edson D. [UNESP]2014-05-272014-05-272013-06-10Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 87, n. 6, 2013.1539-37551550-2376http://hdl.handle.net/11449/75626We 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. © 2013 American Physical Society.engArea-preserving mappingsChaotic orbitsControl parametersDiffusion equationsPeriodic orbitsScaling invarianceSurvival probabilitiesTransport of particlesHamiltoniansMappingPhase space methodsTwo dimensionalDiffusionArtigo10.1103/PhysRevE.87.062904WOS:000320166600014Acesso restrito2-s2.0-848795407702-s2.0-84879540770.pdf6130644232718610