A family of dissipative two-dimensional mappings: Chaotic, regular and steady state dynamics investigation

Some dynamical properties for a family of two dimensional mappings controlled by three parameters are considered in this paper. For null dissipation and depending on the other control parameters, diffusion in phase space is observed. A connection with the standard mapping is made to determine the range of control parameters leading to unlimited diffusion. In the dissipative case, for low nonlinearity, we obtain the fixed points and an expression to find any periodic orbit with any period, if it exists. For large nonlinearity we investigate the Lyapunov exponents and characterise the steady state of the system for a long time.