Transactions of the American Mathematical Society

Author(s): T. Fisher; M. Rodriguez Hertz
Journal: Trans. Amer. Math. Soc. 361 (2009), 3707-3720.
MSC (2000): Primary 37D05, 37D20
Posted: February 10, 2009
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Abstract: In 1969, Hirsch posed the following problem: given a diffeomorphism $f:N\to N$ and a compact invariant hyperbolic set $\Lambda$ of

, describe the topology of $\Lambda$ and the dynamics of

restricted to $\Lambda$ . We solve the problem where $\Lambda=M^3$ is a closed

-manifold: if

is orientable, then it is a connected sum of tori and handles; otherwise it is a connected sum of tori and handles quotiented by involutions.

The dynamics of the diffeomorphisms restricted to

, called quasi-Anosov diffeomorphisms, is also classified: it is the connected sum of DA-diffeomorphisms, quotiented by commuting involutions.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 37D05, 37D20

T. Fisher
Affiliation: Department of Mathematics, Brigham Young University, 292 TMCB, Provo, Utah 84602
Email: tfisher@math.byu.edu

M. Rodriguez Hertz
Affiliation: IMERL, Facultad de Ingeniería, University de la Republica, Julio Herrera y Reissig 565, 11300 Montevideo, Uruguay
Email: jana@fing.edu.uy

DOI: 10.1090/S0002-9947-09-04687-X
PII: S 0002-9947(09)04687-X
Keywords: Dynamical systems, hyperbolic set, robustly expansive, quasi-Anosov
Received by editor(s): May 8, 2007
Posted: February 10, 2009
Additional Notes: This work was partially supported by NSF Grant \#DMS0240049, Fondo Clemente Estable 9021 and PDT
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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