Geodesic
Existence of invariant curves for maps close to degenerate maps, and a~solution of the~Fermi--Ulam problem
Sbornik. Mathematics, Tome 82 (1995) no. 1, pp. 231-241

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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. 
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     author = {L. D. Pustyl'nikov},
     title = {Existence of invariant curves for maps close to degenerate maps, and a~solution of {the~Fermi--Ulam} problem},
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     language = {en},
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L. D. Pustyl'nikov. Existence of invariant curves for maps close to degenerate maps, and a~solution of the~Fermi--Ulam problem. Sbornik. Mathematics, Tome 82 (1995) no. 1, pp. 231-241. http://geodesic.mathdoc.fr/item/SM_1995_82_1_a11/