| we analyze the recurrence - time statistics ( rts ) in three - dimensional non - hamiltonian volume preserving systems ( vps ) : an extended standard map , and a fluid model . the extended map is a standard map weakly coupled to an extra - dimension which contains a deterministic regular , mixed ( regular and chaotic ) or chaotic motion . the extra - dimension strongly enhances the trapping times inducing plateaus and distinct algebraic and exponential decays in the rts plots . the combined analysis of the rts with the classification of ordered and chaotic regimes and scaling properties , allows us to describe the intricate way trajectories penetrate the before impenetrable regular islands from the uncoupled case . essentially the plateaus found in the rts are related to trajectories that stay long times inside trapping tubes , not allowing recurrences , and then penetrates diffusively the islands ( from the uncoupled case ) by a diffusive motion along such tubes in the extra - dimension . all asymptotic exponential decays for the rts are related to an ordered regime ( quasi - regular motion ) and a mixing dynamics is conjectured for the model . these results are compared to the rts of the standard map with dissipation or noise , showing the peculiarities obtained by using three - dimensional vps . we also analyze the rts for a fluid model and show remarkable similarities to the rts in the extended standard map problem . |