The Anosov relation for Nielsen numbers of maps of infra-nilmanifolds

DOI10.1007/s00605-006-0409-5zbMath1112.55002OpenAlexW2143092687MaRDI QIDQ870656

Bram De Rock, Wim Malfait, Karel Dekimpe

Publication date: 13 March 2007

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-006-0409-5

zbMATH Keywords

Nielsen numberLefschetz numberinfra-nilmanifoldexpanding mapAnosov theorem

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Fixed points and coincidences in algebraic topology (55M20)

Related Items (5)

Nielsen zeta functions for maps on infra-nilmanifolds are rational ⋮ Coincidence theory for infra-nilmanifolds ⋮ The Nielsen and Reidemeister numbers of maps on infra-solvmanifolds of type \((\mathrm{R})\) ⋮ HOMOTOPY MINIMAL PERIODS FOR HYPERBOLIC MAPS ON INFRA-NILMANIFOLDS ⋮ Averaging Formula for Nielsen Numbers of Maps on Infra-Solvmanifolds of Type (R)

Uses Software

• CARAT
• AClib

Cites Work

• Unnamed Item
• The Anosov theorem for flat generalized Hantzsche-Wendt manifolds
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• The Anosov theorem for infranilmanifolds with an odd-order Abelian holonomy group
• Expanding endomorphisms of flat manifolds
• Almost-Bieberbach groups: affine and polynomial structures
• The Nielsen numbers of virtually unipotent maps on infra-nilmanifolds
• Lectures on Nielsen fixed point theory
• The Nielsen numbers of maps of nil-manifolds
• The Nielsen numbers of Anosov diffeomorphisms on flat Riemannian manifolds
• Expanding maps on 2-step infra-nilmanifolds

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