## 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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