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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Real bounds, ergodicity and negative Schwarzian for multimodal maps
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by Sebastian van Strien and Edson Vargas PDF
J. Amer. Math. Soc. 17 (2004), 749-782 Request permission

Erratum: J. Amer. Math. Soc. 20 (2007), 267-268.


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:
  • Edson Vargas
  • Affiliation: Department of Mathematics, University of São Paulo, São Paulo, Brazil
  • Email:
  • 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)
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 17 (2004), 749-782
  • MSC (2000): Primary 37Exx, 37Fxx
  • DOI:
  • MathSciNet review: 2083467