Minimal number of periodic points for C1 self-maps of compact simply-connected manifolds

被引：24

作者：

Graff, Grzegorz ^{[1
]}

Jezierski, Jerzy ^{[2
]}

机构：

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

[2] Warsaw Univ Life Sci SGGW, Dept Math & Informat, PL-02757 Warsaw, Poland

来源：

FORUM MATHEMATICUM | 2009年 / 21卷 / 03期

关键词：

FIBER TECHNIQUES; WECKENS THEOREM; SOLVMANIFOLDS; ITERATIONS; DIMENSION; INDEXES; NIL;

D O I：

10.1515/FORUM.2009.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let f be a self-map of a smooth compact connected and simply-connected manifold of dimension m >= 3, r a fixed natural number. In this paper we define a topological invariant D-r(m)[f] which is the best lower bound for the number of r-periodic points for all C-1 maps homotopic to f. In case m = 3 we give the formula for D-r(3)[f] and calculate it for self-maps of S-2 x I.

引用

页码：491 / 509

页数：19

共 32 条

[1] Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
Grzegorz Graff
Jerzy Jezierski
[J]. Geometriae Dedicata, 2017, 187 : 241 - 258
[2] AN ALGORITHMIC APPROACH TO ESTIMATING THE MINIMAL NUMBER OF PERIODIC POINTS FOR SMOOTH SELF-MAPS OF SIMPLY-CONNECTED MANIFOLDS
Graff, Grzegorz
Pilarczyk, Pawel
[J]. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2015, 45 (01) : 273 - 286
[3] Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
Graff, Grzegorz
Jezierski, Jerzy
[J]. GEOMETRIAE DEDICATA, 2017, 187 (01) : 241 - 258
[4] Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers
Graff, Grzegorz
Kaczkowska, Agnieszka
[J]. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2012, 10 (06): : 2160 - 2172
[5] MINIMIZATION OF THE NUMBER OF PERIODIC POINTS FOR SMOOTH SELF-MAPS OF CLOSED SIMPLY-CONNECTED 4-MANIFOLDS
Graff, Grzegorz
Jezierski, Jerzy
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 31 : 523 - 532
[6] COMPUTATIONS OF THE LEAST NUMBER OF PERIODIC POINTS OF SMOOTH BOUNDARY-PRESERVING SELF-MAPS OF SIMPLY-CONNECTED MANIFOLDS
Graff, Grzegorz
Jezierski, Jerzy
Myszkowski, Adrian
[J]. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2020, 56 (02) : 589 - 606
[7] Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds
Grzegorz Graff
Jerzy Jezierski
[J]. Journal of Fixed Point Theory and Applications, 2013, 13 : 63 - 84
[8] Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds
Graff, Grzegorz
Jezierski, Jerzy
[J]. JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2013, 13 (01) : 63 - 84
[9] C1 SELF-MAPS ON CLOSED MANIFOLDS WITH ALL THEIR PERIODIC POINTS HYPERBOLIC
Llibre, Jaume
Sirvent, Victor F.
[J]. HOUSTON JOURNAL OF MATHEMATICS, 2015, 41 (04): : 1119 - 1127
[10] Degrees of Self-Maps of Simply Connected Manifolds
Amann, Manuel
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (18) : 8545 - 8589

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