The main goal of this book is to present and discuss many of the common scaling properties
observed in some nonlinear dynamical systems described by mappings. The …

A dynamical phase transition from integrability to non-integrability for a family of 2-D
Hamiltonian mappings whose angle, θ, diverges in the limit of vanishingly action, I, is …

We show that, in strongly chaotic dynamical systems, the average particle velocity can be
calculated analytically by consideration of Brownian dynamics in a phase space, the method …

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 …

A family of dissipative two-dimensional nonlinear mappings is considered. The mapping is
described by the angle and action variables and parameterized by ε controlling nonlinearity …

The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit
of vanishingly action is investigated by using the solution of the diffusion equation. The …

The chaotic diffusion for particles moving in a time dependent potential well is described by
using two different procedures:(i) via direct evolution of the mapping describing the …

A new universal empirical function that depends on a single critical exponent (acceleration
exponent) is proposed to describe the scaling behavior in a dissipative kicked rotator. The …

We have shown that a break of symmetry of the probability distribution and a biased random
walk behavior lead the dynamics of a two dimensional mapping to present unlimited …

The main goal of this book is to discuss some scaling properties and characterize twophase
transitions in nonlinear systems described by mappings. The chaotic dynamics is given by …