Hyperbolicity of renormalization for critical circle maps with non-integer exponents

Igors Gorbovickis, Michael Yampolsky

Published 2015-05-04Version 1

We construct a renormalization operator which acts on analytic circle maps whose critical exponent $\alpha$ is not necessarily an odd integer $2n+1$, $n\in\mathbb N$. When $\alpha=2n+1$, our definition generalizes cylinder renormalization of analytic critical circle maps. In the case when $\alpha$ is close to an odd integer, we prove hyperbolicity of renormalization for maps of bounded type.