Universality from resonance renormalization of Hamiltonian maps (Q1070617)

The following is paraphrased from the author's introduction. ''The Hamiltonian for a single island chain (pth-resonance) of the standard mapping is obtained using secular perturbation theory and the method of averaging. A local standard mapping is reconstituted, approximately, for a single island of that chain. The relation between the stochasticity parameter \(\bar K\) of the local mapping, and the parameter K of the original mapping is obtained, which constitutes a renormalization of p mapping iterations. Setting \(\bar K=K\) then determines a value of K for which each p-island chain is self-similar in all orders.''