Institute for Mathematical Sciences

Preprint ims01-04

A. Epstein and M. Yampolsky
A universal parabolic map.

Abstract: Parabolic renormalization of critical circle maps arises as a degenerate case of the usual renormalization when the periods of the renormalized maps become infinite. In the paper we give new proofs of the main renormalization conjectures for the parabolic case, which are notably simplier than those required in the usual case. The title of the paper refers to the attracting fixed point of the parabolic renormalization, whose existence we prove.
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