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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F11%3A%230000288" target="_blank" >RIV/47813059:19610/11:#0000288 - isvavai.cz</a>

Result on the web

—

DOI - Digital Object Identifier

—

Result language

angličtina

Original language name

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

Original language 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 weformulate it at the end of the paper.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

—

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2011

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Ergodic Theory and Dynamical Systems

ISSN

0143-3857

e-ISSN

—

Volume of the periodical

31

Issue of the periodical within the volume

1

Country of publishing house

GB - UNITED KINGDOM

Number of pages

11

Pages from-to

—

UT code for WoS article

000286013200009

EID of the result in the Scopus database

—