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Complex bounds for renormalization of critical circle maps

Published online by Cambridge University Press:  01 February 1999

MICHAEL YAMPOLSKY
MICHAEL YAMPOLSKY
Affiliation:
Mathematics Department, Yale University, New Haven, CT 06520-8283, USA (e-mail: [email protected])
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Abstract

We use the methods developed with Lyubich for proving complex bounds for real quadratics to extend 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.

As another application of our methods we present a new proof of a theorem of Petersen on local connectivity of some Siegel Julia sets.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 1 , February 1999 , pp. 227 - 257
Copyright
1999 Cambridge University Press

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Footnotes

This is an expanded version of the paper ‘Complex bounds for critical circle maps’, which appeared as IMS Stony Brook Preprint 95-12.