Institute for Mathematical Sciences
Complex Bounds for Critical Circle Maps
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.
View ims95-12 (PDF format)