American Institute of Mathematical Sciences

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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

Jacopo De Simoi 1,

1. 

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

Received  July 2008 Revised  March 2009 Published  August 2009

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