Leis de escala no mapa padrão dissipativo - Vicente, Anderson Ricardo [UNESP] (2016)
Some dynamical properties for the dissipative standard map are studied. The map is described by two dynamical variables, namely and corresponding respectively to the action and angle variables. The model is characterized by two control parameters: (i) is responsible for controlling the nonlinearity of the system and; (ii) controlling the intensity of the dissipation of the system. For = 0 the results for the Taylor-Chirikov standard map are recovered. It means that for a non-dissipative case and, depending on the parameter , the phase space of the system is mixed therefore showing periodic islands, invariant spanning curves and chaos. When > = 0,9716…, the invariant spanning curves are destroyed and the variable action can spread without limits over the phase space. When ≠ 0 the system is called dissipative; chaotic attractors appear in the phase space and there is a suppression of the unlimited dissemination of the variable action in the phase space. We investigate the dynamics of the standard map in the neighboring of two transitions: (i) local chaos to global chaos and; (ii) limited growth of action to unlimited growth of action. We show the behavior of the average quadratic actions () determined by the critical exponents that characterize the dynamics near the transition of unlimited diffusion to limited diffusion of the variable action using two methods: (I) phenomenological and; (II) analytical