Nekhoroshev Stability Estimates for Symplectic Maps and Physical Applications
The Nekhoroshev stability estimates for symplectic maps of R 2d are presented. After an illustration of the basic ideas in a simple hamiltonian model, the dynamics of a charged particle in the magnetic lattice of an accelerator is considered and it is shown to be conveniently described by a symplectic map. After recalling the basic properties of the Birkhoff normal forms, we state a general theorem on the stability of the orbits and sketch the proof. The factorial divergence of the Birkhoff series appears to arise from nonlinearity as well as from the divisors, and a functional equation with interesting analytic properties is obtained from the majorant series.
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