Minimizing the number of periodic points for smooth maps. Non-simply connected case

DOI10.1016/j.topol.2010.11.002zbMath1211.55004OpenAlexW1984621444MaRDI QIDQ624390

Grzegorz Graff, Jerzy Jezierski

Publication date: 9 February 2011

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

Full work available at URL: https://doi.org/10.1016/j.topol.2010.11.002

zbMATH Keywords

Nielsen numberperiodic pointsmooth mapindices of iterations

Mathematics Subject Classification ID

Fixed-point and coincidence theorems (topological aspects) (54H25) 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 (13)

A sufficient condition for the realizability of the least number of periodic points of a smooth map ⋮ Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds ⋮ Periodic points of self-maps of products of lens spaces \(L(3)\times L(3)\) ⋮ Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers ⋮ Some developments in Nielsen fixed point theory ⋮ When a smooth self-map of a semi-simple Lie group can realize the least number of periodic points ⋮ Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds ⋮ Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces ⋮ The least number, of \(n\)-periodic points of a self-map of a solvmanifold, can be realised by a smooth map ⋮ Minimal number of periodic points for smooth self-maps of \(\mathbb {R}P^3\) ⋮ Least number of periodic points of self-maps of Lie groups ⋮ Least number of \(n\)-periodic points of self-maps of \(PSU(2)\times PSU(2)\) ⋮ Dold sequences, periodic points, and dynamics

Cites Work

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• Fixed point indices of iterations of \(C^1\) maps in \(\mathbb R^3\)
• Fixed point indices of iterated maps
• Homotopy periodic sets of selfmaps of real projective spaces
• Wecken's theorem for periodic points in dimension at least 3
• Minimal number of periodic points for smooth self-maps of S³
• Minimal number of periodic points for C 1 self-maps of compact simply-connected manifolds
• Lectures on Nielsen fixed point theory
• Twisted Burnside-Frobenius theory for discrete groups

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