Minimal number of periodic points for C 1 self-maps of compact simply-connected manifolds

DOI10.1515/FORUM.2009.023zbMath1173.37014MaRDI QIDQ3632758

Jerzy Jezierski, Grzegorz Graff

Publication date: 12 June 2009

Published in: Forum Mathematicum (Search for Journal in Brave)

zbMATH Keywords

fixed point indexLefschetz numberiterated map

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) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (17)

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 ⋮ Self-maps of \(S^2\) homotopic to a smooth map with a single \(n\)-periodic point ⋮ 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 ⋮ Minimizing the number of periodic points for smooth maps. Non-simply connected case ⋮ 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 ⋮ Fixed point indices of iterated smooth maps in arbitrary dimension ⋮ The least number of 2-periodic points of a smooth self-map of \({S}^{2}\) of degree 2 equals 2 ⋮ Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds ⋮ 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 ⋮ Minimal number of periodic points for smooth self-maps of \(\mathbb {R}P^3\) ⋮ Dynamics of field line mappings in magnetic flux tubes ⋮ Least number of periodic points of self-maps of Lie groups ⋮ Least number of \(n\)-periodic points of self-maps of \(PSU(2)\times PSU(2)\)

Cites Work

• Fixed point indices of iterations of \(C^1\) maps in \(\mathbb R^3\)
• Fixed point indices of iterated maps
• A remark on the Lefschetz fixed point formula for differentiable maps
• Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds. I
• Finding periodic points of a map by use of a \(k\)-adic expansion
• Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds. II
• Wecken's theorem for periodic points in dimension at least 3
• THE BEHAVIOR OF THE INDEX OF PERIODIC POINTS UNDER ITERATIONS OF A MAPPING
• Weak Wecken's theorem for periodic points in dimension 3

This page was built for publication: Minimal number of periodic points for C 1 self-maps of compact simply-connected manifolds