Stability and instability results in a model of Fermi acceleration

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September 2009, 25(3): 719-750. doi: 10.3934/dcds.2009.25.719

Stability and instability results in a model of Fermi acceleration

1.	Dept. of Mathematics, College Park, MD 20740, United States

Received July 2008 Revised March 2009 Published August 2009

Abstract
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We consider the static wall approximation to the dynamics of a particle bouncing on a periodically oscillating infinitely heavy plate while subject to a potential force. We assume the case of a potential given by a power of the height of the particle and sinusoidal motions of the plate. We find that for powers smaller than 1 the set of escaping orbits has full Hausdorff dimension for all motions and we obtain existence of elliptic islands of period 2 for arbitrarily high energies for a full-measure set of motions. Moreover, we find conditions on the potential to ensure that the total (Lebesgue) measure of elliptic islands of period 2 is either finite or infinite.

Keywords: Dimension Theory, Elliptic islands., Fermi Acceleration, Escaping orbits.

Mathematics Subject Classification: Primary: 37D25; Secondary: 37J40, 37J25, 70H1.

Citation: Jacopo De Simoi. Stability and instability results in a model of Fermi acceleration. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 719-750. doi: 10.3934/dcds.2009.25.719

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