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January  2007, 18(1): 39-52. doi: 10.3934/dcds.2007.18.39

Examples of Anosov Lie algebras

Meera G. Mainkar 1, and  Cynthia E. Will 2,

1. 

Department of Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada
2. 

FaMAF and CIEM, Universidad Nacional de Córdoba, Haya de la Torre s/n, 5000 Córdoba, Argentina

Received  June 2006 Revised  December 2006 Published  February 2007

We construct new families of examples of (real) Anosov Lie algebras, starting with algebraic units. We also give examples of indecomposable Anosov Lie algebras (not a direct sum of proper Lie ideals) of dimension $13$ and $16$, and we conclude that for every $n \geq 6$ with $n \ne 7$ there exists an indecomposable Anosov Lie algebra of dimension $n$.
Keywords: Anosov diffeomorphisms, hyperbolic automorphisms., nilmanifolds, nilpotent Lie algebras.
Mathematics Subject Classification: Primary: 37D20; Secondary: 22E25, 20F3.
Citation: Meera G. Mainkar, Cynthia E. Will. Examples of Anosov Lie algebras. Discrete & Continuous Dynamical Systems, 2007, 18 (1) : 39-52. doi: 10.3934/dcds.2007.18.39
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