On the growth of the number of periodic points for smooth self-maps of a compact manifold

被引：5

作者：

Graff, Grzegorz

Jezierski, Jerzy

机构：

[1] Gdansk Univ Technol, Fac Appl Phys & Math, PL-80952 Gdansk, Poland

[2] Warsaw Univ Life Sci, SGGW, Inst Appl Math, PL-00757 Warsaw, Poland

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 135卷 / 10期

关键词：

periodic points; C-1; maps; indices of iterations; Nielsen number;

D O I：

10.1090/S0002-9939-07-08836-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let f be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension m >= 3. We show that in the homotopy class of f there is a C-1 map with less then r periodic points, up to any given fixed period r.

引用

页码：3249 / 3254

页数：6

共 10 条

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

BABENKO, IK ;

BOGATYI, SA .

MATHEMATICS OF THE USSR-IZVESTIYA, 1992, 38 (01) :1-26

[2]

Brown R. F., 1971, LEFSCHETZ FIXED POIN

[3]

Chow S.N., 1983, SPRINGER LECT NOTES, V1007, P109

[4] FIXED-POINT INDEXES OF ITERATED MAPS [J].

DOLD, A .

INVENTIONES MATHEMATICAE, 1983, 74 (03) :419-435

[5]

DOLD A, 1983, LECT ALGEBRAIC TOPOL

[6]

Graff G, 2006, DISCRETE CONT DYN-A, V16, P843

[7]

JEZIERSKI J., 2005, TOPOLOGICAL FIXED PO, V3

[8] Wecken's theorem for periodic points in dimension at least 3 [J].

Jezierski, Jerzy .

TOPOLOGY AND ITS APPLICATIONS, 2006, 153 (11) :1825-1837

[9] Generic diffeomorphisms with superexponential growth of number of periodic orbits [J].

Kaloshin, VY .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 211 (01) :253-271

[10]

Shub Michael, 1974, TOPOLOGY, V13, P189

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