Universality in the transition to chaos of dissipative systems (Q1081930)

A thorough study of the effect of dissipation is set forth here. The first two sections deal with the physical model used to perform the numerical investigation and the ''experimental'' data thus obtained. A study of the renormalization process enables to generalise the relation \(\delta_ n(J)=\delta_{n-1}(J^ 2)\), first given by \textit{A. B. Zisook} [Commun. Math. Phys. 96, 361-371 (1984; Zbl 0586.70008)], to all transforms where the Jacobian does not depend on the linearization point in the phase space. Furthermore a first order approximation gives an excellent analytic expression of the universal function displaying the crossover of the decrement between \(\delta\) (II) and \(\delta\) (I).