Abstract
We define an analytic setting for renormalization of unimodal maps with an arbitrary critical exponent. We prove the global hyperbolicity of renormalization conjecture for unimodal maps of bounded type with a critical exponent which is sufficiently close to an even integer. Furthermore, we prove the global \(C^{1+\beta }\)-rigidity conjecture for such maps, giving the first example of a smooth rigidity theorem for unimodal maps whose critical exponent is not an even integer.
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MY was partially supported by NSERC Discovery Grant.
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Gorbovickis, I., Yampolsky, M. Renormalization for Unimodal Maps with Non-integer Exponents. Arnold Math J. 4, 179–191 (2018). https://doi.org/10.1007/s40598-018-0089-y
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DOI: https://doi.org/10.1007/s40598-018-0089-y