Intermittency in connected hamiltonian systems

Intermittency, as extensively examined in dissipative systems, is studied in hamiltonian systems consisting of integrable or chaotic billiards connected through a hole. Near the transition to intermittency we obtain the scaling law 〈τ〉∝|p−pc|−1, where 〈τ〉 is the mean residence time in a billiard, p is d or A−1 (d: hole length, A: area of the billiard, dc=A−1c=0). In cases with particular geometrical distortions in the neighborhood of the hole, this law holds if d is replaced by a conveniently defined effective hole size. This work is a first step for studying chaotic scattering systems whose exits are connected to confining potentials.