caa a22 4500 445849401 CHVBK 20180317145409.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s10240-011-0034-2 doi (NATIONALLICENCE)springer-10.1007/s10240-011-0034-2 The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes [Elektronische Daten] [Artur Avila, Mikhail Lyubich] We prove exponential contraction of renormalization along hybrid classes of infinitely renormalizable unimodal maps (with arbitrary combinatorics), in any even degree d. We then conclude that orbits of renormalization are asymptotic to the full renormalization horseshoe, which we construct. Our argument for exponential contraction is based on a precompactness property of the renormalization operator ("beau bounds”), which is leveraged in the abstract analysis of holomorphic iteration. Besides greater generality, it yields a unified approach to all combinatorics and degrees: there is no need to account for the varied geometric details of the dynamics, which were the typical source of contraction in previous restricted proofs. IHES and Springer-Verlag, 2011 Avila Artur CNRS UMR 7586, Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, 75013, Paris, France aut Lyubich Mikhail Department of Mathematics, Stony Brook University, 11794-3651, Stony Brook, NY, USA aut Publications mathématiques de l'IHÉS Springer-Verlag 114/1(2011-11-01), 171-223 0073-8301 114:1<171 2011 114 10240 https://doi.org/10.1007/s10240-011-0034-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10240-011-0034-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Avila Artur CNRS UMR 7586, Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, 75013, Paris, France aut NATIONALLICENCE 700 1- Lyubich Mikhail Department of Mathematics, Stony Brook University, 11794-3651, Stony Brook, NY, USA aut NATIONALLICENCE 773 0- Publications mathématiques de l'IHÉS Springer-Verlag 114/1(2011-11-01), 171-223 0073-8301 114:1<171 2011 114 10240 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer