Transport properties in the discontinuous dissipative standard mapping

Abstract

The dissipative two-dimensional nonlinear mapping that describes a kicked rotator given by a rigid bar of length L with one end attached by a pivot and the other end subjected to a vertical and periodic impulsive discontinuous force has the following form [1] In+1 = (1 − γ)In + kf (θn ) sin(θn ), T : (1) θn+1 = [θn + In+1 ] mod (2π) where I and θ are the action and angle variables, k and γ are control parameters responsible for controlling the intensity of nonlinearity and dissipation respectively. Figure 1 shows the phase space using control parameters k = 102 and γ = 10−3 which we observe chaotic attractors. The I ∗ is an approximation of the maximum value of the chaotic attractors. [...]