Dissipation and its consequences in the scaling exponents for a family of two-dimensional mappings

Abstract

The effects and consequences of dissipation in the scaling exponents describing the behaviour of average properties over the chaotic dynamics for a family of two-dimensional mappings are studied. The mapping is parametrized by an exponent γ in one of the dynamical variables and by a parameter δ ∈ [0, 1], which denotes the amount of the dissipation. The Lyapunov exponents are obtained for different values of γ and δ in the range 0 < δ < 1. The behaviour of the approaching orbits to the chaotic attractors is described analytically to be of exponential type. The deviation around the average action for chaotic orbits was described by a single set of scaling exponents obtained for different γ leading the model to fall into the same universality class as that of the dissipative bouncer model.

Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps

“…1(b) and 2(b). This exponential decay of action (and related quantities) has also been reported for dissipative maps in [6,32,35]. Moreover, from Eq.…”

“…In fact, n CO was correctly reported to be proportional to γ −1 in [6,9,11,12,15,32,34,35], when γ 1, for several dissipative maps.…”