"3"^^ . . "[AE83BF857CBD]" . "M\u00E1lek, Michal" . . . . . . "0143-3857" . . "Z(MSM4781305904)" . "Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites"@en . "Ergodic Theory and Dynamical Systems" . . . "RIV/47813059:19610/11:#0000288" . "RIV/47813059:19610/11:#0000288!RIV11-MSM-19610___" . . "Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites" . "Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites"@en . "11"^^ . . "19610" . . "Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites" . "000286013200009" . "Ko\u010Dan, Zden\u011Bk" . "entropy; horseshoe; homoclinic trajectory; tree; graph; dendrite"@en . "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 . . . "Korneck\u00E1-Kurkov\u00E1, Veronika" . . . . . . "197654" . . "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." . . "1" . "31" . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . "3"^^ .