A. Celletti, G. Della Penna, C. Froeschle'
Analytical approximation of the solution of the dissipative standard map
(259K, Postscript)
ABSTRACT. We consider a dissipative mapping derived from a
modification of the Chirikov standard mapping. For definiteness,
we assume that the dissipative strenght is of the order of the
square of the perturbing parameter of the conservative model.
Under this simplifying assumption, we derive an analytical
approximation of the solutions associated to the dissipative
mapping. The equations are explicitely 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 values of the perturbing parameter, while they get
different as the break--down threshold of the invariant curve
with rotation number $\omega$ is approached.