Contents

Several authors have observed that heuristic probabilistic arguments suggest that no divergent trajectories occur.

If a divergent trajectory exists, it cannot be equidistributed . Indeed if one defines

then it can be proved that the condition (2.30) implies thatTheorem F constrains the possible behavior of divergent trajectories. Indeed, associated to any divergent trajectory is the infinite set and for all . Since for all , Theorem F implies that

where . Roughly speaking, (2.32) asserts that the elements of a divergent trajectory cannot go to infinity ``too slowly.''Contents