Analytical approximation of the solution of the dissipative standard map

We consider a dissipative mapping derived from a modification of the Chirik ov standard map ping. For simplicity, we assume that the dissipative streng th is of the order of the square of the perturbing parameter of the conserv ative model. Under this assumption, we derive an analytical approximation o f the solution associated to the dissipative mapping. The equations are exp licitly solved up to the order 7 in the perturbing parameter. Having fixed a frequency omega, a comparison of the associated conservative and dissipative solutions shows that the two curves coincide for low value s of the perturbing parameter, while in most cases they diverge as the brea kdown threshold of the invariant curve with rotation number omega is approa ched.