Quasiperiodic Perturbation of a Symplectic Map

Stathis Tompaidis from the University of Texas at Austin, writes

Numerical Study of Invariant Sets of a
Quasiperiodic Perturbation of a Symplectic Map


We study the behavior of invariant sets of a volume­-preserving
map that is a quasiperiodic perturbation of a symplectic map,
using approximation by periodic orbits. We present numerical
results for analyticity domains of invariant surfaces, behavior
after breakdown, and a critical function describing breakdown
of invariant surfaces as a function of their rotation vectors. We
discuss implications of our results to the existence of a renor-­
malization group operator describing breakdown of invariant
surfaces.

The quasiperiodicity of mathematics, may describe physical systems. I studied a mapping with symmetry five for the harmonic oscillator, periodically kicked. By no means do we know all there is to know on quasiperiodicity.