Periodic points of self-maps of a space with π1X=Zps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _1X=\mathbb {Z}_{p^s}$$\end{document}

被引：0

作者：

Jerzy Jezierski ^{[1
]}

Xuezhi Zhao ^{[2
]}

机构：

[1] Warsaw University of Life Sciences (SGGW),Institute of Applications of Informatics and Mathematics

[2] Capital Normal University,School of Mathematical Sciences

来源：

Journal of Fixed Point Theory and Applications | 2025年 / 27卷 / 1期

关键词：

Periodic points; Nielsen number; least number of periodic points; fixed point index; group ; Primary 55M20; Secondary 37C05; 37C25;

D O I：

10.1007/s11784-024-01155-2

中图分类号：

学科分类号：

摘要：

The crucial homotopy invariants in Nielsen periodic point theory are numbers: NPn(f)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$NP_n(f)$$\end{document}, which is a lower bound of the number of periodic points of length n, and NFn(f)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$NF_n(f)$$\end{document} a lower bound of the number of periodic points of length dividing n. Here, f:X→X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f:X\rightarrow X$$\end{document} is a self-map of a compact polyhedron. We derive formulae of the invariants for self-maps of polyhedra with fundamental group π1M=Zps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _1 M=\mathbb {Z}_{p^s}$$\end{document} whose all irreducible classes are essential.

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