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Existence of unique SRB-measures is typical for real unicritical polynomial families

Bruin, H, Shen, WX and Van Strien, S (2006) Existence of unique SRB-measures is typical for real unicritical polynomial families ANN SCI ECOLE NORM S, 39 (3). 381 - 414. ISSN 0012-9593

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Abstract

We show that for a one-parameter family of unicritical polynomials {fc} with even critical order ℓ⩾2, for almost all parameters c, fc admits a unique SRB-measure, being either absolutely continuous, or supported on the postcritical set. As a by product we prove that if fc has a Cantor attractor, then it is uniquely ergodic on its postcritical set.

Item Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Annales Scientifiques de l’École Normale Supérieure. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Annales Scientifiques de l’École Normale Supérieure, 39(3), May 2006,DOI 10.1016/j.ansens.2006.02.001/.
Uncontrolled Keywords: UNIMODAL MAPS, INVARIANT-MEASURES, NEGATIVE SCHWARZIAN, QUADRATIC MAPS, CANTOR SETS, DYNAMICS, ATTRACTORS, GEOMETRY, DECAY
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Symplectic Elements
Date Deposited: 25 Jan 2012 14:43
Last Modified: 23 Sep 2013 18:55
URI: http://epubs.surrey.ac.uk/id/eprint/37234

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