On Limit Sets of Monotone Maps on Dendroids

被引：1

作者：

Makhrova, E. N. ^{[1
]}

机构：

[1] Lobachevsky State Univ Nizhny Novgorod, Nizhnii Novgorod, Nizhny Novgorod, Russia

来源：

APPLIED MATHEMATICS AND NONLINEAR SCIENCES | 2020年 / 5卷 / 02期

关键词：

dendroid; dendrite; monotone map; periodic point; non-wandering point; omega-limit set; DYNAMICS; DENDRITE;

D O I：

10.2478/AMNS.2020.2.00056

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a dendrite, f : X -> X be a monotone map. In the papers by I. Naghmouchi (2011, 2012) it is shown that omega-limit set omega(x, f) of any point x is an element of X has the next properties: (1) omega(x, f) subset of <(Per(f))over bar>, where Per(f) is the sei of periodic points of f; (2) omega(x, f) is either a periodic orbit or a minimal Cantor set. In the paper by E. Makhrova, K. Vaniukova (2016) it is proved that (3) Omega(F) = <(Per(f))over bar>, where Omega(f) is the set of non-wandering points of f . The aim of this note is to show that the above results (1) - (3) do not hold for monotone maps on dendroids.

引用

页码：311 / 316

页数：6

共 13 条

[1]

Balibrea F, 2002, DISCRETE CONT DYN S, V8, P983

[2]

Balibrea F., 2001, J DYN SYST-T ASME, V3, P87

[3] A characterization of adding machine maps [J].

Block, L ;

Keesling, J .

TOPOLOGY AND ITS APPLICATIONS, 2004, 140 (2-3) :151-161

[4] LIAPUNOV STABILITY AND ADDING MACHINES [J].

BUESCU, J ;

STEWART, I .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1995, 15 :271-290

[5] Dynamics of skew products of interval maps [J].

Efremova, L. S. .

RUSSIAN MATHEMATICAL SURVEYS, 2017, 72 (01) :101-178

[6] Differential properties and attracting sets of a simplest skew product of interval maps [J].

Efremova, L. S. .

SBORNIK MATHEMATICS, 2010, 201 (06) :873-907

[7]

Kocen Z., 1999, ANN MATH SIL, V13, P181

[8] ON DYNAMICS OF TRIANGULAR MAPS OF THE SQUARE [J].

KOLYADA, SF .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1992, 12 :749-768

[9]

Kuratovski K., 1968, TOPOLOGY, V2

[10] On the set of non-wandering points of monotone maps on local dendrites [J].

Makhrova, E. N. ;

Vaniukova, K. S. .

NOMA15 INTERNATIONAL WORKSHOP ON NONLINEAR MAPS AND APPLICATIONS, 2016, 692

← 1 2 →