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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

Dmitry Dolgopyat 1,

1. 

Department of Mathematics University of Maryland, College Park MD 21742

Received  February 2007 Revised  May 2007 Published  June 2008

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