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On algebraic Anosov diffeomorphisms on nilmanifolds. (Russian, English) Zbl 1097.37016
Sib. Mat. Zh. 45, No. 5, 995-1021 (2004); translation in Sib. Math. J. 45, No. 5, 821-839 (2004).
Summary: The article is devoted to the algebraic approaches to Anosov diffeomorphisms. All examples of Anosov diffeomorphisms known so far are connected directly or indirectly with compact nilmanifolds. We consider some new necessary conditions for the existence of these diffeomorphisms on nilmanifolds. We demonstrate the absence of Anosov diffeomorphisms on some classes of nilmanifolds. We prove some results on Lie groups and lattices in them, too.

MSC:
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
20F18 Nilpotent groups
22E25 Nilpotent and solvable Lie groups
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