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Statements

Subject Item
n2:RIV%2F47813059%3A19610%2F11%3A%230000288%21RIV11-MSM-19610___
rdf:type
skos:Concept n7:Vysledek
dcterms:description
It is known that the positiveness of topological entropy, the existence of a horseshoe and the existence of a homoclinic trajectory are mutually equivalent, for interval maps. The aim of the paper is to investigate the relations between the properties for continuous maps of trees, graphs and dendrites. We consider three different definitions of a horseshoe and two different definitions of a homoclinic trajectory. All the properties are mutually equivalent for tree maps, whereas not for maps on graphs and dendrites. For example, positive topological entropy and the existence of a homoclinic trajectory are independent and neither of them implies the existence of any horseshoe in the case of dendrites. Unfortunately, there is still an open problem, and we formulate it at the end of the paper. It is known that the positiveness of topological entropy, the existence of a horseshoe and the existence of a homoclinic trajectory are mutually equivalent, for interval maps. The aim of the paper is to investigate the relations between the properties for continuous maps of trees, graphs and dendrites. We consider three different definitions of a horseshoe and two different definitions of a homoclinic trajectory. All the properties are mutually equivalent for tree maps, whereas not for maps on graphs and dendrites. For example, positive topological entropy and the existence of a homoclinic trajectory are independent and neither of them implies the existence of any horseshoe in the case of dendrites. Unfortunately, there is still an open problem, and we formulate it at the end of the paper.
dcterms:title
Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites
skos:prefLabel
Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites
skos:notation
RIV/47813059:19610/11:#0000288!RIV11-MSM-19610___
n7:predkladatel
n8:orjk%3A19610
n3:aktivita
n14:Z
n3:aktivity
Z(MSM4781305904)
n3:cisloPeriodika
1
n3:dodaniDat
n12:2011
n3:domaciTvurceVysledku
n4:4661842 n4:8981310 n4:4012429
n3:druhVysledku
n17:J
n3:duvernostUdaju
n10:S
n3:entitaPredkladatele
n18:predkladatel
n3:idSjednocenehoVysledku
197654
n3:idVysledku
RIV/47813059:19610/11:#0000288
n3:jazykVysledku
n19:eng
n3:klicovaSlova
entropy; horseshoe; homoclinic trajectory; tree; graph; dendrite
n3:klicoveSlovo
n6:horseshoe n6:graph n6:dendrite n6:homoclinic%20trajectory n6:entropy n6:tree
n3:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n3:kontrolniKodProRIV
[AE83BF857CBD]
n3:nazevZdroje
Ergodic Theory and Dynamical Systems
n3:obor
n5:BA
n3:pocetDomacichTvurcuVysledku
3
n3:pocetTvurcuVysledku
3
n3:rokUplatneniVysledku
n12:2011
n3:svazekPeriodika
31
n3:tvurceVysledku
Málek, Michal Kočan, Zdeněk Kornecká-Kurková, Veronika
n3:wos
000286013200009
n3:zamer
n15:MSM4781305904
s:issn
0143-3857
s:numberOfPages
11
n16:organizacniJednotka
19610