Minimal sets of periods for maps on the Klein bottle

被引：7

作者：

Kim, Ju Young ^{[1
]}

Kim, Sung Sook ^{[2
]}

Zhao, Xuezhi ^{[3
]}

机构：

[1] Catholic Univ Daegu, Dept Math, Taegu 712702, South Korea

[2] Paichai Univ, Dept Appl Math, Taejon 302735, South Korea

[3] Capital Normal Univ, Dept Math, Beijing 100037, Peoples R China

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2008年 / 45卷 / 03期

关键词：

periodic point; minimum set of periods; Nielsen number; Klein bottle;

D O I：

10.4134/JKMS.2008.45.3.883

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main results concern with the self maps on the Klein bottle. We obtain the Reidemeister numbers and the Nielsen numbers for all self maps on the Klein bottle. In terms of the Nielsen numbers of their iterates, we totally determine the minimal sets of periods for all homotopy classes of self maps on the Klein bottle.

引用

页码：883 / 902

页数：20

共 50 条

[21] Homotopy minimal periods for nilmanifold maps
Jerzy Jezierski
Waclaw Marzantowicz
Mathematische Zeitschrift, 2002, 239 : 381 - 414
[22] Homotopy minimal periods for nilmanifold maps
Jezierski, J
Marzantowicz, WA
MATHEMATISCHE ZEITSCHRIFT, 2002, 239 (02) : 381 - 414
[23] Minimal sets of antitriangular maps
Balibrea, F
Linero, A
Canovas, JS
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (07): : 1733 - 1741
[24] MINIMAL SETS OF MAPS OF Y
ALSEDA, L
YE, XD
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1994, 187 (01) : 324 - 338
[25] Wecken type problems for self-maps of the Klein bottle
DL Gonçalves
MR Kelly
Fixed Point Theory and Applications, 2006
[26] Wecken type problems for self-maps of the Klein bottle
Goncalves, D. L.
Kelly, M. R.
FIXED POINT THEORY AND APPLICATIONS, 2006, 2006 (1)
[27] Semi-equivelar maps on the torus and the Klein bottle are Archimedean
Datta, Basudeb
Maity, Dipendu
DISCRETE MATHEMATICS, 2018, 341 (12) : 3296 - 3309
[28] Enumeration of doubly semi-equivelar maps on the Klein bottle
Singh, Yogendra
Tiwari, Anand Kumar
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2023,
[29] CLASSIFICATION OF CLOSED LOCALLY MINIMAL NETWORKS ON FLAT KLEIN BOTTLE
PTITSINA, IV
VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1995, (02): : 15 - 22
[30] Sets of Periods for Expanding Maps on Flat Manifolds
Roberto Tauraso
Monatshefte für Mathematik, 1999, 128 : 151 - 157

← 1 2 3 4 5 →