EXISTENCE OF INVARIANT CURVES FOR MAPS CLOSE TO DEGENERATE MAPS, AND A SOLUTION OF THE FERMI-ULAM PROBLEM

Abstract

The Ulam model is studied in this paper: a small elastic ball moves vertically between two infinitely heavy horizontal walls, each of which moves in the vertical direction according to a periodic law. It is proved that the velocity of the ball is always bounded. The proof is based on a generalization of Moser's theorem on the existence of invariant curves under an area preserving mapping of an annulus. Bibliography: 16 titles.