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• W2743806489 endingPage "1119" @default.
• W2743806489 startingPage "1001" @default.
• W2743806489 abstract "In this paper we prove complex bounds, also referred to as a priori bounds for C 3, and, in particular, for analytic maps of the interval. Any C 3 mapping of the interval has an asymptotically holomorphic extension to a neighbourhood of the interval. We associate to such a map, a complex box mapping, which provides a kind of Markov structure for the dynamics. Moreover, we prove universal geometric bounds on the shape of the domains and on the moduli between components of the range and domain. Such bounds show that the first return maps to these domains are well controlled, and consequently such bounds form one of the corner stones in many recent results in one-dimensional dynamics, for example: renormalization theory, rigidity, density of hyperbolicity, and local connectivity of Julia sets." @default.
• W2743806489 created "2017-08-17" @default.
• W2743806489 creator A5028849443 @default.
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• W2743806489 date "2017-08-12" @default.
• W2743806489 modified "2023-10-04" @default.
• W2743806489 title "Complex Bounds for Real Maps" @default.
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• W2743806489 doi "https://doi.org/10.1007/s00220-017-2958-y" @default.
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