Dynamical properties of a dissipative discontinuous map: A scaling investigation

The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action as a function of the n-th iteration of the map as well as the parameters K and gamma, controlling nonlinearity and dissipation, respectively. We concentrate our efforts to study the case where the nonlinearity is large; i.e., K >> 1. In this regime and for large initial action I-0 >> K, we prove that dissipation produces an exponential decay for the average action . Also, for I-0 congruent to 0, we describe the behavior of using a scaling function and analytically obtain critical exponents which are used to overlap different curves of onto a universal plot. We complete our study with the analysis of the scaling properties of the deviation around the average action omega. (C) 2013 Elsevier B.V. All rights reserved.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq