Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds

被引：10

作者：

Graff, Grzegorz ^{[1
]}

Jezierski, Jerzy ^{[2
]}

机构：

[1] Gdansk Univ Technol, Fac Appl Phys & Math, Narutowicza 11-12, PL-80233 Gdansk, Poland

[2] Warsaw Univ Life Sci SGGW, Inst Applicat Math, Nowoursynowska 159, PL-00757 Warsaw, Poland

来源：

GEOMETRIAE DEDICATA | 2017年 / 187卷 / 01期

关键词：

Periodic points; Boundary-preserving maps; Nielsen number; Fixed point index; Smooth maps; NIELSEN TYPE NUMBERS; INDEXES; ITERATIONS;

D O I：

10.1007/s10711-016-0199-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be a smooth compact and simply-connected manifold with simply-connected boundary , r be a fixed odd natural number. We consider f, a self-map of M, preserving . Under the assumption that the dimension of M is at least 4, we define an invariant that is equal to the minimal number of r-periodic points for all maps preserving and -homotopic to f. As an application, we give necessary and sufficient conditions for a reduction of a set of r-periodic points to one point in the -homotopy class.

引用

页码：241 / 258

页数：18

共 26 条

[1] THE BEHAVIOR OF THE INDEX OF PERIODIC POINTS UNDER ITERATIONS OF A MAPPING [J].