  The correlation integral and determinism are quantitative characteristics of
a dynamical system based on the recurrence of orbits. For strongly non-chaotic
interval maps, the determinism equals 1 for every small enough threshold. This
means that trajectories of such systems are perfectly predictable in the
infinite horizon. In this paper we study the correlation integral and
determinism for the family of $2^\infty$ non-chaotic maps, first considered by
Delahaye in 1980. The determinism in a finite horizon equals 1. However, the
behaviour of the determinism in the infinite horizon is counter-intuitive.
Sharp bounds on the determinism are provided.
