Expanding maps, Anosov diffeomorphisms and affine structures on infra-nilmanifolds

  • Dekimpe K
  • Lee K
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Abstract

In this paper we present a complete description of Lie algebras admitting an expanding and/or a hyperbolic automorphism in terms of ℝ-gradings of these Lie algebras. Using this, we then show that any infra-nilmanifold which admits an expanding map or an Anosov diffeomorphism also has a complete, affinely flat structure. © 2002 Elsevier Science B.V. All rights reserved.

Author-supplied keywords

  • Anosov diffeomorphism
  • Expanding map
  • Graded Lie algebra
  • Hyperbolic automorphism
  • Nilpotent Lie algebra

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Authors

  • Karel Dekimpe

  • Kyung Bai Lee

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