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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On structurally stable diffeomorphisms with codimension one expanding attractors


Authors: V. Grines and E. Zhuzhoma
Journal: Trans. Amer. Math. Soc. 357 (2005), 617-667
MSC (2000): Primary 37D20; Secondary 37C70, 37C15
Published electronically: April 16, 2004
MathSciNet review: 2095625
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Abstract: We show that if a closed $n$-manifold $M^n$ $(n\ge 3)$ admits a structurally stable diffeomorphism $f$ with an orientable expanding attractor $\Omega$ of codimension one, then $M^n$ is homotopy equivalent to the $n$-torus $T^n$ and is homeomorphic to $T^n$ for $n\ne 4$. Moreover, there are no nontrivial basic sets of $f$ different from $\Omega$. This allows us to classify, up to conjugacy, structurally stable diffeomorphisms having codimension one orientable expanding attractors and contracting repellers on $T^n$, $n\ge 3$.


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Additional Information

V. Grines
Affiliation: Department of Mathematics, Agriculture Academy of Nizhny Novgorod, 97 Gagarin Ave, Nizhny Novgorod, 603107 Russia

E. Zhuzhoma
Affiliation: Department of Applied Mathematics, Nizhny Novgorod State Technical University, 24 Minina Str., Nizhny Novgorod, 603600 Russia
Email: zhuzhoma@mail.ru

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03460-9
PII: S 0002-9947(04)03460-9
Received by editor(s): March 15, 2001
Received by editor(s) in revised form: April 10, 2003, and July 10, 2003
Published electronically: April 16, 2004
Additional Notes: This research was partially supported by the RFFI grant 02-01-00098
Article copyright: © Copyright 2004 American Mathematical Society