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Existence of unique SRB-measures is typical for real unicritical polynomial families
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Bruin, Henk, Shen, Weixiao and Strien, Sebastian van (2006) Existence of unique SRB-measures is typical for real unicritical polynomial families. Annales Scientifiques de l'Ecole Normale Superieure, Vol.39 (No.3). pp. 381-414. doi:10.1016/j.ansens.2006.02.001 ISSN 0012-9593.
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Official URL: http://dx.doi.org/10.1016/j.ansens.2006.02.001
Abstract
We show that for a one-parameter family of unicritical polynomials {f(c)} with even critical order l >= 2, for almost all parameters c, f(c), admits a unique SRB-measure, being either absolutely continuous, or supported on the postcritical set. As a byproduct we prove that if f(c) has a Cantor attractor, then it is uniquely ergodic on its postcritical set. (c) 2006 Published by Elsevier Masson SAS.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Annales Scientifiques de l'Ecole Normale Superieure | ||||
Publisher: | Societe Mathematique de France | ||||
ISSN: | 0012-9593 | ||||
Official Date: | May 2006 | ||||
Dates: |
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Volume: | Vol.39 | ||||
Number: | No.3 | ||||
Number of Pages: | 34 | ||||
Page Range: | pp. 381-414 | ||||
DOI: | 10.1016/j.ansens.2006.02.001 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | GR/S91147/01, GR/R73171/01 |
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