Transactions of the American Mathematical Society

On structurally stable diffeomorphisms with codimension one expanding attractors

Author(s): V. Grines; E. Zhuzhoma
Journal: Trans. Amer. Math. Soc. 357 (2005), 617-667.
MSC (2000): Primary 37D20; Secondary 37C70, 37C15
Posted: April 16, 2004
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Abstract: We show that if a closed

-manifold

$(n\ge 3)$ admits a structurally stable diffeomorphism

with an orientable expanding attractor $\Omega$ of codimension one, then

is homotopy equivalent to the

-torus

and is homeomorphic to

for $n\ne 4$ . Moreover, there are no nontrivial basic sets of

different from $\Omega$ . This allows us to classify, up to conjugacy, structurally stable diffeomorphisms having codimension one orientable expanding attractors and contracting repellers on

, $n\ge 3$ .

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 37D20, 37C70, 37C15

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: 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
Posted: April 16, 2004
Additional Notes: This research was partially supported by the RFFI grant 02-01-00098
Copyright of article: Copyright 2004, American Mathematical Society

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