Yampolsky, Michael The attractor of renormalization and rigidity of towers of critical circle maps. (English) Zbl 0978.37033 Commun. Math. Phys. 218, No. 3, 537-568 (2001). 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. Reviewer: Messoud Efendiev (Berlin) Cited in 1 ReviewCited in 22 Documents MSC: 37E20 Universality and renormalization of dynamical systems Keywords:universality; global attractor PDFBibTeX XMLCite \textit{M. Yampolsky}, Commun. Math. Phys. 218, No. 3, 537--568 (2001; Zbl 0978.37033) Full Text: DOI arXiv