Monday, March 25, 2013

1303.5510 (Maxim Arnold et al.)

Pinball dynamics: unlimited energy growth in nonsmooth/switching
Hamiltonian systems

Maxim Arnold, Vadim Zharnitsky
A family of discontinuous symplectic maps on the cylinder is considered. This family arises naturally in nonsmooth Hamiltonian dynamics and in switched Hamiltonian systems. The transformation depends on two parameters and is a canonical model for the study of bounded and unbounded behavior in discontinuous mappings due to nonlinear resonances. This paper provides a general description of the map and presents one case of an unbounded orbit.
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