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

H Bruin; WX Shen; S Van Strien

doi:10.1016/j.ansens.2006.02.001

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

Journal article

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Peer reviewed

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

H Bruin, WX Shen and S Van Strien

ANN SCI ECOLE NORM S, Vol.39(3), pp.381-414

05/2006

DOI: https://doi.org/10.1016/j.ansens.2006.02.001

Abstract

UNIMODAL MAPS

INVARIANT-MEASURES

NEGATIVE SCHWARZIAN

QUADRATIC MAPS

CANTOR SETS

DYNAMICS

ATTRACTORS

GEOMETRY

DECAY

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.

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Title: Existence of unique SRB-measures is typical for real unicritical polynomial families
Creators: H Bruin
WX Shen
S Van Strien
Publication Details: ANN SCI ECOLE NORM S, Vol.39(3), pp.381-414
Publisher: GAUTHIER-VILLARS/EDITIONS ELSEVIER
Date published: 05/2006
Date submitted: 05/12/2011
Identifiers: 99514943002346
Academic Unit: Department of Mathematics
Language: English
Resource Type: Journal article

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

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