HOMOTOPY MINIMAL PERIODS FOR HYPERBOLIC MAPS ON INFRA-NILMANIFOLDS

DOI10.1017/nmj.2017.15zbMath1420.55004OpenAlexW2611404263MaRDI QIDQ3119526

Gert-Jan Dugardein, Karel Dekimpe

Publication date: 12 March 2019

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/nmj.2017.15

zbMATH Keywords

infra-nilmanifoldminimal periodshyperbolic maps

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)

Cites Work

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• Nielsen zeta functions for maps on infra-nilmanifolds are rational
• The finiteness of the Reidemeister number of morphisms between almost-crystallographic groups.
• The Anosov relation for Nielsen numbers of maps of infra-nilmanifolds
• Homotopy minimal periods for expanding maps on infra-nilmanifolds
• Asymptotics of the discrete spectrum for certain operators in \({\mathbb{R}}^ d\)
• Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds. I
• Homotopy minimal periods for nilmanifold maps
• Maps on infra-nilmanifolds. Rigidity and applications to fixed-point theory
• Minimal sets of periods for torus maps via Nielsen numbers
• Lefschetz numbers for continuous maps, and periods for expanding maps on infra-nilmanifolds
• The Nielsen and Reidemeister numbers of maps on infra-solvmanifolds of type \((\mathrm{R})\)
• On the cohomology of compact homogeneous spaces of nilpotent Lie groups
• Lectures on Nielsen fixed point theory
• Dynamical zeta functions, Nielsen theory and Reidemeister torsion
• Differentiable dynamical systems

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