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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Topological structure of (partially) hyperbolic sets with positive volume
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by José F. Alves and Vilton Pinheiro PDF
Trans. Amer. Math. Soc. 360 (2008), 5551-5569 Request permission


We consider both hyperbolic sets and partially hyperbolic sets attracting a set of points with positive volume in a Riemannian manifold. We obtain several results on the topological structure of such sets for diffeomorphisms whose differentiability is larger than one. We show in particular that there are no partially hyperbolic horseshoes with positive volume for such diffeomorphisms. We also give a description of the limit set of almost every point belonging to a hyperbolic set or a partially hyperbolic set with positive volume.
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Additional Information
  • José F. Alves
  • Affiliation: Departamento de Matemática Pura, Faculdade de Ciências do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
  • Email:
  • Vilton Pinheiro
  • Affiliation: Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil
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  • Received by editor(s): June 5, 2006
  • Received by editor(s) in revised form: January 8, 2007
  • Published electronically: April 28, 2008
  • Additional Notes: This work was carried out at the Federal University of Bahia, University of Porto and IMPA. The first author was partially supported by CMUP, by a grant of FCT and by POCI/MAT/61237/2004. The second author was partially supported by PADCT/CNPq and by POCI/MAT/61237/2004
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 5551-5569
  • MSC (2000): Primary 37Dxx
  • DOI:
  • MathSciNet review: 2415085