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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Real bounds, ergodicity and negative Schwarzian for multimodal maps


Authors: Sebastian van Strien and Edson Vargas
Journal: J. Amer. Math. Soc. 17 (2004), 749-782
MSC (2000): Primary 37Exx, 37Fxx
Published electronically: August 27, 2004
Erratum: J. Amer. Math. Soc. 20 (2007), 267--268
MathSciNet review: 2083467
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Abstract: We consider smooth multimodal maps which have finitely many non-flat critical points. We prove the existence of real bounds. From this we obtain a new proof for the non-existence of wandering intervals, derive extremely useful improved Koebe principles, show that high iterates have `negative Schwarzian derivative' and give results on ergodic properties of the map. One of the main complications in the proofs is that we allow $f$ to have inflection points.


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Additional Information

Sebastian van Strien
Affiliation: Department of Mathematics, Warwick University, Coventry CV4 7AL, England
Email: strien@maths.warwick.ac.uk

Edson Vargas
Affiliation: Department of Mathematics, University of São Paulo, São Paulo, Brazil
Email: vargas@ime.usp.br

DOI: http://dx.doi.org/10.1090/S0894-0347-04-00463-1
PII: S 0894-0347(04)00463-1
Keywords: Dynamical systems, interval dynamics, holomorphic dynamics
Received by editor(s): May 1, 2002
Published electronically: August 27, 2004
Additional Notes: The first author was partially supported by EPSRC grant GR/R73171/01.
The second author was partially supported by CNPq-Brasil, Grant #300557/89-2(RN)
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.