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Real bounds, ergodicity and negative Schwarzian for multimodal maps
Author(s):
Sebastian
van Strien;
Edson
Vargas
Journal:
J. Amer. Math. Soc.
17
(2004),
749-782.
MSC (2000):
Primary 37Exx, 37Fxx
Posted:
August 27, 2004
Errata:
J. Amer. Math. Soc. 20 (2007), 267--268
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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  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:
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
Posted:
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)
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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