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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Hyperbolic automorphisms and Anosov diffeomorphisms on nilmanifolds

Author: Karel Dekimpe
Journal: Trans. Amer. Math. Soc. 353 (2001), 2859-2877
MSC (2000): Primary 37D20; Secondary 20F18, 20F34
Published electronically: March 14, 2001
MathSciNet review: 1828476
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Abstract | References | Similar Articles | Additional Information


We translate the problem of finding Anosov diffeomorphisms on a nilmanifold which is covered by a free nilpotent Lie group into a problem of constructing matrices in $\mathrm{GL}(n,\mathbb{Z})$ whose eigenvalues satisfy certain conditions. Afterwards, we show how this translation can then be solved in some specific situations. The paper starts with a section on polynomial permutations of $\mathbb{Q}^K$, a subject which is of interest on its own.

References [Enhancements On Off] (What's this?)

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Additional Information

Karel Dekimpe
Affiliation: Katholieke Universiteit Leuven, Campus Kortrijk, B-8500 Kortrijk, Belgium

Received by editor(s): January 17, 1999
Received by editor(s) in revised form: January 31, 2000
Published electronically: March 14, 2001
Additional Notes: Postdoctoral Fellow of the Fund for Scientific Research - Flanders (F.W.O.)
Article copyright: © Copyright 2001 American Mathematical Society