---
abstract: |
    We use the methods developed with M. Lyubich for proving complex bounds for real quadratics to extend E. De Faria's complex a priori bounds to all critical circle maps with an irrational rotation number. The contracting property for renormalizations of critical circle maps follows.\
    In the Appendix we give an application of the complex bounds for proving local connectivity of some Julia sets.
author:
- Michael Yampolsky
title: Complex Bounds for Critical Circle Maps
---

\[section\] \[thm\]<span>Corollary</span> \[thm\]<span>Lemma</span> \[thm\]<span>Proposition</span>

\[section\]

\[section\]

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{'source': 'arXiv_out/math9510219_extract_Main'}