Rigidity, universality,and hyperbolicity of renormalization for critical circle maps with non-integer exponents

Igors Gorbovickis, Michael Yampolsky

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…