Stochastic solutions in a conservative dynamic system

It is known that solutions of autonomous fourth order conservative dynamic systems, or second order non autonomous dynamic systems, with periodic coefficients can be described by an autonomous second order point mapping (a second order recurrence or surface transformation). The recurrence considered in this paper, which arises in the study of particle dynamics in accelerators and storage rings, is x/sub n+1/=y /sub n/+F(x/sub n/), y/sub n+1/=-x/sub n/+F(x/sub n+1/), F(0)=0 with F (x)= mu x+(1- mu )x/sup alpha /, -1< mu <1, alpha =2 and 3. The qualitative behaviour of the solutions, some of which are 'stochastic', is examined. (9 refs).