The Nielsen and Reidemeister numbers of maps on infra-solvmanifolds of type \((\mathrm{R})\)

DOI10.1016/j.topol.2014.12.003zbMath1346.37021arXiv1303.0784OpenAlexW2537862402MaRDI QIDQ2512648

Jong Bum Lee, Alexander Fel'shtyn

Publication date: 30 January 2015

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.0784

zbMATH Keywords

Nielsen numberNielsen zeta functioninfra-nilmanifoldReidemeister numberReidemeister zeta functioninfra-solvmanifold of type \((\mathrm R)\)

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (19)

Nielsen spectrum of maps on infra-solvmanifolds modeled on $Sol_0^{kern2pt 4}$ ⋮ Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups ⋮ Unnamed Item ⋮ Algorithms for twisted conjugacy classes of polycyclic-by-finite groups ⋮ Reidemeister zeta functions of low-dimensional almost-crystallographic groups are rational ⋮ Pólya-Carlson dichotomy for coincidence Reidemeister zeta functions via profinite completions ⋮ Calculation of Nielsen periodic numbers on infra-solvmanifolds of type (R) ⋮ Dynamical zeta functions of Reidemeister type and representations spaces ⋮ Dynamical zeta functions of Reidemeister type ⋮ Nielsen coincidence theory on infra-solvmanifolds of Sol ⋮ Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds ⋮ Density of the homotopy minimal periods of maps on infra-solvmanifolds ⋮ The Nielsen numbers of iterations of maps on infra-solvmanifolds of type (R) and periodic orbits ⋮ Nielsen zeta functions on infra-nilmanifolds up to dimension three ⋮ The \(R_\infty\) property for crystallographic groups of Sol ⋮ HOMOTOPY MINIMAL PERIODS FOR HYPERBOLIC MAPS ON INFRA-NILMANIFOLDS ⋮ Strongly scale-invariant virtually polycyclic groups ⋮ Dold sequences, periodic points, and dynamics ⋮ An averaging formula for Nielsen numbers on infra-solvmanifolds

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