On structurally stable diffeomorphisms with codimension one expanding attractors

被引：26

作者：

Grines, V

Zhuzhoma, E

机构：

[1] Agr Acad Nizhny Novgorod, Dept Math, Nizhnii Novgorod 603107, Russia

[2] Nizhny Novgorod State Tech Univ, Dept Appl Math, Nizhnii Novgorod 603600, Russia

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 357卷 / 02期

关键词：

D O I：

10.1090/S0002-9947-04-03460-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that if a closed n-manifold M-n (n greater than or equal to 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 not equal 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 greater than or equal to 3.

引用

页码：617 / 667

页数：51