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Название: Asymptotic Geometry of Hyperbolic Well-Ordered Cantor Sets
Авторы: Tangerman F.M., Veerman J.J.P.
In this paper we study the well-ordered Cantor sets in hyperbolic sets on the line and the plane. Examples of such sets occur in circle maps and in areapreserving twist maps. We set up a renormalization scheme employing in both cases the first return map. We prove convergence of this scheme. The convergence implies that the asymptotic geometry of such a well-ordered set with irrational rotation number and their nearby well-ordered orbits is determined by the Lyapunov exponent of this set.