We prove exponential contraction of renormalization along hybrid classes ofinfinitely renormalizable unimodal maps (with arbitrary combinatorics), in anyeven degree $d$. We then conclude that orbits of renormalization are asymptoticto the full renormalization horseshoe, which we construct. Our argument forexponential contraction is based on a precompactness property of therenormalization operator ("beau bounds"), which is leveraged in the abstractanalysis of holomorphic iteration. Besides greater generality, it yields aunified approach to all combinatorics and degrees: there is no need to accountfor the varied geometric details of the dynamics, which were the typical sourceof contraction in previous restricted proofs.
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机译：我们证明了无限重可标准化的单峰图（具有任意组合）的混合类的重归一化的指数收缩，其度数为$ d $。然后我们得出结论，重新规范化的轨道对于我们构建的完整的重新规范化马蹄形是渐近的。我们关于指数收缩的论据基于归一化算子的“预紧性”属性（“美丽界限”），该属性在全纯迭代的抽象分析中得到了利用。除了具有更大的通用性之外，它还为所有组合度和度数提供了统一的方法：无需考虑动力学的各种几何细节，而这是以前的受限证明中典型的收缩源。
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