Wecken property for periodic points on the Klein bottle
Keywords
Periodic point, homotopy minimal period, Nielsen number, Nielsen-Jiang periodic number, Klein bottleAbstract
Suppose $f\colon M\to M$ on a compact manifold. Let $m$ be a natural number. One of the most important questions in the topological theory of periodic points is whether the Nielsen-Jiang periodic number $NF_m(f)$ is a sharp lower bound on $\# \text{\rm Fix}(g^m)$ over all $g\sim f$. This question has a positive answer if $\text{\rm dim} M\geq 3$ but in general a negative answer for self maps of compact surfaces. However, we show the answer to be positive when $M={\mathbb K}$ is the Klein bottle. As a consequence, we reconfirm a result of Llibre and compute the set $\text{\rm HPer} (f)$ of homotopy minimal periods on the Klein bottle.Downloads
Published
2009-03-01
How to Cite
1.
JEZIERSKI, Jerzy, KEPPELMANN, Edward and MARZANTOWICZ, Wacław. Wecken property for periodic points on the Klein bottle. Topological Methods in Nonlinear Analysis. Online. 1 March 2009. Vol. 33, no. 1, pp. 51 - 64. [Accessed 28 March 2024].
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