The anosov theorem for infranilmanifolds with an odd-order abelian holonomy group

We prove that "Equation missing" for any continuous map "Equation missing" of a given infranilmanifold with Abelian holonomy group of odd order. This theorem is the analogue of a theorem of Anosov for continuous maps on nilmanifolds. We will also show that although their fundamen...

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Bibliographic Details
Published in:Fixed point theory and applications (Hindawi Publishing Corporation) 2006-01, Vol.2006 (1), Article 63939
Main Authors: Dekimpe, K, De Rock, B, Pouseele, H
Format: Article
Language:English
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Summary:We prove that "Equation missing" for any continuous map "Equation missing" of a given infranilmanifold with Abelian holonomy group of odd order. This theorem is the analogue of a theorem of Anosov for continuous maps on nilmanifolds. We will also show that although their fundamental groups are solvable, the infranilmanifolds we consider are in general not solvmanifolds, and hence they cannot be treated using the techniques developed for solvmanifolds.
ISSN:1687-1812
1687-1820
1687-1812
DOI:10.1155/FPTA/2006/63939