Solenoidal attractors with bounded combinatorics are shy

Pages 1-79 from Volume 191 (2020), Issue 1 by Daniel Smania

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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Keywords
, , , , , ,
Mathematical Subject Classification
Primary: , , , , ,
DOI
https://doi.org/10.4007/annals.2020.191.1.1
MR
4045962
zbMATH
07154425
Milestones
Received: 22 March 2016
Revised: 3 May 2019
Accepted: 22 July 2019
Published online: 30 December 2019

Authors

Daniel Smania

Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo-Campus de São Carlos, São Carlos-SP, Brazil