Metric attractors for smooth unimodal maps

Jacek Graczyk; Duncan Sands; Grzegorz Świątek

doi:https://doi.org/10.4007/annals.2004.159.725

Pages 725-740 from Volume 159 (2004), Issue 2 by Jacek Graczyk, Duncan Sands, Grzegorz Świątek

Abstract

We classify the measure theoretic attractors of general $C^3$ unimodal maps with quadratic critical points. The main ingredient is the decay of geometry.

Mathematical Subject Classification

Primary 2000: 37E05 Secondary: 37C70, 37D45

Milestones

Received: 20 June 2001
Accepted: 24 January 2002
Published online: March 2004

Authors

Jacek Graczyk

Département de Mathématiques, University of Paris XI, 91405 Orsay, France

Duncan Sands

Département de Mathématiques, University of Paris XI, 91405 Orsay, France

Grzegorz Świątek

Mathematics Department, Pennsylvania State University, University Park, State College, PA 16802, United States