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The attractor of renormalization and rigidity of towers of critical circle maps. (English) Zbl 0978.37033

This paper is devoted to the universality in one-dimensional dynamics, found in critical circle maps. The author proves the existence of a global attractor \(\mathcal A\) with a Cantor set structure for the renormalization of critical circle mappings. The set \(\mathcal A\) is invariant under a generalized renormalization transformation, whose action on \(\mathcal A\) is conjugate to the two-sided shift with a countable alphabet.

MSC:

37E20 Universality and renormalization of dynamical systems
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