Lefschetz numbers for continuous maps, and periods for expanding maps on infra-nilmanifolds

DOI10.1016/j.geomphys.2005.11.003zbMath1109.55001OpenAlexW2085517395MaRDI QIDQ2507658

Jong Bum Lee, Kyung Bai Lee

Publication date: 5 October 2006

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2005.11.003

zbMATH Keywords

periodic pointsinfra-nilmanifoldsexpanding mapsNielsen numbers

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) Discontinuous groups of transformations (57S30)

Related Items (18)

Nielsen spectrum of maps on infra-solvmanifolds modeled on $Sol_0^{kern2pt 4}$ ⋮ Unnamed Item ⋮ Formulas for the Reidemeister, Lefschetz and Nielsen coincidence number of maps between infra-nilmanifolds ⋮ Calculation of Nielsen periodic numbers on infra-solvmanifolds of type (R) ⋮ Homotopy minimal period self-maps on flat manifolds ⋮ Growth rate for endomorphisms of finitely generated nilpotent groups ⋮ The finiteness of the Reidemeister number of morphisms between almost-crystallographic groups. ⋮ Calculation of Nielsen periodic numbers on infra-nilmanifolds ⋮ Nielsen coincidence theory on infra-solvmanifolds of Sol ⋮ Averaging formula for Nielsen coincidence numbers ⋮ Density of the homotopy minimal periods of maps on infra-solvmanifolds ⋮ Coincidence theory for infra-nilmanifolds ⋮ The Anosov theorem for infranilmanifolds with an odd-order Abelian holonomy group ⋮ Eventually periodic points of infra-nil endomorphisms ⋮ The Nielsen numbers of iterations of maps on infra-solvmanifolds of type (R) and periodic orbits ⋮ 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)

Cites Work

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• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• On algebraic numbers of small height: Linear forms in one logarithm
• Minimal sets of periods for torus maps
• Sets of periods for expanding maps on flat manifolds
• Maps on infra-nilmanifolds. Rigidity and applications to fixed-point theory
• 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 Homotopically Periodic Maps of Infranilmanifolds
• Nielsen Numbers of Maps of Tori
• Expanding maps on infra-nilmanifolds of homogeneous type
• Endomorphisms of Compact Differentiable Manifolds
• Averaging Formula for Nielsen Numbers

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