Abstract
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.
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