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Topological structure of (partially) hyperbolic sets with positive volume
Author(s):
José
F.
Alves;
Vilton
Pinheiro
Journal:
Trans. Amer. Math. Soc.
360
(2008),
5551-5569.
MSC (2000):
Primary 37Dxx
Posted:
April 28, 2008
MathSciNet review:
2415085
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Abstract:
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:
jfalves@fc.up.pt
Vilton
Pinheiro
Affiliation:
Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil
Email:
viltonj@ufba.br
DOI:
10.1090/S0002-9947-08-04484-X
PII:
S 0002-9947(08)04484-X
Keywords:
Hyperbolic set,
partially hyperbolic set,
horseshoe
Received by editor(s):
June 5, 2006
Received by editor(s) in revised form:
January 8, 2007
Posted:
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 of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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