Bouncing balls in non-linear potentials

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January & February 2008, 22(1&2): 165-182. doi: 10.3934/dcds.2008.22.165

Bouncing balls in non-linear potentials

1.	Department of Mathematics University of Maryland, College Park MD 21742

Received February 2007 Revised May 2007 Published June 2008

Abstract
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We consider a ball bouncing off infinitely heavy periodically moving plate in the presence of a potential force. Assuming that the potential equals to a power of the ball's height we present conditions guaranteeing recurrence in the sense that the total energy of almost every trajectory does not go to infinity.

Keywords: slow-fast systems, KAM theory, invariant cones, martingales..

Mathematics Subject Classification: Primary: 37D25; Secondary: 37J40, 70D05, 70H1.

Citation: Dmitry Dolgopyat. Bouncing balls in non-linear potentials. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 165-182. doi: 10.3934/dcds.2008.22.165

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