Exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant tori
An approximate renormalisation scheme is derived for the breakup of invariant tori of arbitrary winding ratio in Hamiltonian systems of one and a half degrees of freedom, similar to that of Escande and Doveil. It is a free semi-group with two generators. This scheme is solved exactly for its orbits, stable manifolds, unstable manifolds and critical set. Various results are found, including a Cantor set of universal fractal diagrams, the robustness of noble tori, and a scaling law for areas near critical circles.
scientific article; zbMATH DE number 4086595