Recurrence time in the homoclinic tangle

We find the minimum recurrence time for the lobes of an unstable periodic orbit (i.e. the number of iterations required in order that an image of a given lobe intersects itself). This time is much shorter than the usual recurrence time derived by applying Poincaré's theorem. As the energy of the system increases the minimum recurrence time decreases. The minimum recurrence time can be found also when the energy exceeds the escape energy, in which case the usual Poincaré recurrence time is not defined.