EXISTENCE OF INVARIANT CURVES FOR DEGENERATE ALMOST PERIODIC REVERSIBLE MAPPINGS

In this paper we are concerned with the existence of invariant curves for almost periodic reversible mappings with higher order degeneracy of the twist condition. In the proof we use a new variant of the KAM theory, containing an artificial parameter q, 0 < q < 1, which makes the steps of the KAM iteration infinitely small in the speed of function q(n)epsilon, rather than super exponential function.

Automated summary

This paper investigates the existence of invariant curves for almost periodic reversible mappings with higher order degeneracy of the twist condition. A new variant of the KAM theory, involving an artificial parameter q, 0 < q < 1, is used in the proof to ensure that the steps of the KAM iteration become infinitely small in the speed of function q(n)epsilon, rather than a super exponential function.