Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds

被引：6

作者：

Graff, Grzegorz ^{[1
]}

Jezierski, Jerzy ^{[2
]}

机构：

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

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

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2013年 / 13卷 / 01期

关键词：

Periodic points; Nielsen number; fixed point index; smooth maps; NIELSEN TYPE NUMBERS; FIXED-POINTS; ORBITS HIDDEN; INDEXES; R-3-HOMEOMORPHISMS; ITERATIONS;

D O I：

10.1007/s11784-012-0076-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M be a closed smooth connected and simply connected manifold of dimension m at least 3, and let r be a fixed natural number. The topological invariant , defined by the authors in [Forum Math. 21 (2009), 491-509], is equal to the minimal number of r-periodic points in the smooth homotopy class of f, a given self-map of M. In this paper, we present a general combinatorial scheme of computing for arbitrary dimension m a parts per thousand yen 4. Using this approach we calculate the invariant in case r is a product of different odd primes. We also obtain an estimate for from below and above for some other natural numbers r.

引用

页码：63 / 84

页数：22

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