We construct a renormalization operator which acts on analytic circle mapswhose critical exponent $lpha$ is not necessarily an odd integer $2n+1$,$ninmathbb N$. When $lpha=2n+1$, our definition generalizes cylinderrenormalization of analytic critical circle maps. In the case when $lpha$ isclose to an odd integer, we prove hyperbolicity of renormalization for maps ofbounded type. We use it to prove universality and $C^{1+lpha}$-rigidity forsuch maps.
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机译：我们构建一个重整化运营商，在分析圈映射上行动临界指数$ Alpha $不一定是奇数Integer $ 2n + 1 $，$ n in mathbb n $。当$ alpha = 2n + 1 $时，我们的定义概括了分析关键圆形地图的Cylinder1形式。在$ alpha $ isclose到奇数整数的情况下，我们证明了对映射类型的映射重新成型化的双曲性。我们使用它来证明普遍性，并为您的$ C ^ {1 + alpha} $ - 僵局forsuch地图。
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