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

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 gamma in one of the dynamical variables and by a parameter delta is an element of [0, 1], which denotes the amount of the dissipation. The Lyapunov exponents are obtained for different values of gamma and delta in the range 0 < delta < 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 gamma leading the model to fall into the same universality class as that of the dissipative bouncer model.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP