Complex bounds for critical circle maps

Details Complex bounds for critical circle maps Complex bounds for critical circle maps

1995-10-14

arxiv.org/abs/math/9510219v1

Mathematics

Dynamical Systems

Scientific paper

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.

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