Topological entropy and periods of graph maps

被引：3

作者：

Llibre, Jaume ^{[1
]}

Saghin, Radu ^{[2
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Catalonia, Spain

[2] Ctr Recerca Matemat, Catalonia, Spain

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2012年 / 18卷 / 04期

关键词：

graph maps; periodic points; periods; topological entropy; TREES;

D O I：

10.1080/10236198.2011.561202

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a complete description of the set of periods of continuous self-maps on graphs which have zero topological entropy and have all their branching points fixed. As a corollary, we get a criterion for positive topological entropy for continuous self-maps on graphs. We also prove that the results are optimal.

引用

页码：589 / 598

页数：10

共 50 条

[1] HORSESHOES, ENTROPY AND PERIODS FOR GRAPH MAPS
LLIBRE, J
MISIUREWICZ, M
TOPOLOGY, 1993, 32 (03) : 649 - 664
[2] Entropy and periods for continuous graph maps
Jaume Llibre
Víctor F. Sirvent
Computational and Applied Mathematics, 2021, 40
[3] Entropy and periods for continuous graph maps
Llibre, Jaume
Sirvent, Victor F.
COMPUTATIONAL & APPLIED MATHEMATICS, 2021, 40 (08):
[4] On dynamics of graph maps with zero topological entropy
Li, Jian
Oprocha, Piotr
Yang, Yini
Zeng, Tiaoying
NONLINEARITY, 2017, 30 (12) : 4260 - 4276
[5] TOPOLOGICAL ENTROPY, SETS OF PERIODS, AND TRANSITIVITY FOR CIRCLE MAPS
Alseda, Lluis
Bordignon, Liane
Groisman, Jorge
UKRAINIAN MATHEMATICAL JOURNAL, 2024, : 31 - 50
[6] Topological structure and entropy of mixing graph maps
Haranczyk, Grzegorz
Kwietniak, Dominik
Oprocha, Piotr
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2014, 34 : 1587 - 1614
[7] TOPOLOGICAL ENTROPY AND PERIODS OF SELF MAPS ON COMPACT MANIFOLDS
Garcia Guirao, Juan Luis
Llibre, Jaume
HOUSTON JOURNAL OF MATHEMATICS, 2017, 43 (04): : 1337 - 1347
[8] GRAPH MAPS WITH ZERO TOPOLOGICAL ENTROPY AND SEQUENCE ENTROPY PAIRS
Li, Jian
Liang, Xianjuan
Oprocha, Piotr
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (11) : 4757 - 4770
[9] A note on the periodic orbits and topological entropy of graph maps
Alsedà, LL
Juher, D
Mumbrú, P
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (10) : 2941 - 2946
[10] Topological entropy of continuous self-maps on a graph
Juan Luis García Guirao
Jaume Llibre
Wei Gao
Computational and Applied Mathematics, 2019, 38

← 1 2 3 4 5 →