About: Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. (en)
Title	Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites (en)
skos:prefLabel	Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites (en)
skos:notation	RIV/47813059:19610/11:#0000288!RIV11-MSM-19610___
http://linked.open...avai/predkladatel	Matematický ústav v Opavě
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM4781305904)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Kornecká-Kurková, Veronika Kočan, Zdeněk Málek, Michal
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Slezská univerzita v Opavě / Matematický ústav v Opavě
http://linked.open...dnocenehoVysledku	197654
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/11:#0000288
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	entropy; horseshoe; homoclinic trajectory; tree; graph; dendrite (en)
http://linked.open.../riv/klicoveSlovo	graph entropy homoclinic trajectory horseshoe tree dendrite
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[AE83BF857CBD]
http://linked.open...i/riv/nazevZdroje	Ergodic Theory and Dynamical Systems
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	31
http://linked.open...iv/tvurceVysledku	Kornecká-Kurková, Veronika Kočan, Zdeněk Málek, Michal
http://linked.open...ain/vavai/riv/wos	000286013200009
http://linked.open...n/vavai/riv/zamer	Topological and analytical methods in the theory of dynamical systems and mathematical physics
issn	0143-3857
number of pages	11 (xsd:int)
http://localhost/t...ganizacniJednotka	19610
is http://linked.open...avai/riv/vysledek of	Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites

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