January 2020 Solenoidal attractors with bounded combinatorics are shy
Daniel Smania
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Ann. of Math. (2) 191(1): 1-79 (January 2020). DOI: 10.4007/annals.2020.191.1.1

Abstract

We show that in a generic finite-dimensional real-analytic family of real-analytic multimodal maps, the subset of parameters on which the corresponding map has a solenoidal attractor with bounded combinatorics is a set with zero Lebesgue measure.

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Daniel Smania. "Solenoidal attractors with bounded combinatorics are shy." Ann. of Math. (2) 191 (1) 1 - 79, January 2020. https://doi.org/10.4007/annals.2020.191.1.1

Information

Published: January 2020
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2020.191.1.1

Subjects:
Primary: 37C20 , 37D20 , 37E05 , 37E20 , 37F25 , 37L45

Keywords: conjugacy , Hyperbolic , multimodal , renormalization , rigidity , solenoidal attractor , Universality

Rights: Copyright © 2020 Department of Mathematics, Princeton University

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Vol.191 • No. 1 • January 2020
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