A generalized definition of topological entropy

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F18%3AA0000036" target="_blank" >RIV/47813059:19610/18:A0000036 - isvavai.cz</a>

Výsledek na webu

<a href="http://topology.auburn.edu/tp/reprints/v52/" target="_blank" >http://topology.auburn.edu/tp/reprints/v52/</a>

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

A generalized definition of topological entropy

Popis výsledku v původním jazyce

Given an arbitrary (not necessarily continuous) function of a topological space to itself, we associate a non-negative extended real number which we call the continuity entropy of the function. In the case where the space is compact and the function is continuous, the continuity entropy of the map is equal to the usual topological entropy of the map. We show that some of the standard properties of topological entropy hold for continuity entropy, but some do not. We show that for piecewise continuous piecewise monotone maps of the interval the continuity entropy agrees with the entropy dened in Horseshoes and entropy for piecewise continuous piecewise monotone maps by Michal Misiurewicz and Krystina Ziemian Finally, we show that if f is a continuous map of the interval to itself and g is any function of the interval to itself which agrees with f at all but countably many points, then the continuity entropies of f and g are equal.

Název v anglickém jazyce

A generalized definition of topological entropy

Popis výsledku anglicky

Given an arbitrary (not necessarily continuous) function of a topological space to itself, we associate a non-negative extended real number which we call the continuity entropy of the function. In the case where the space is compact and the function is continuous, the continuity entropy of the map is equal to the usual topological entropy of the map. We show that some of the standard properties of topological entropy hold for continuity entropy, but some do not. We show that for piecewise continuous piecewise monotone maps of the interval the continuity entropy agrees with the entropy dened in Horseshoes and entropy for piecewise continuous piecewise monotone maps by Michal Misiurewicz and Krystina Ziemian Finally, we show that if f is a continuous map of the interval to itself and g is any function of the interval to itself which agrees with f at all but countably many points, then the continuity entropies of f and g are equal.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EE2.3.30.0007" target="_blank" >EE2.3.30.0007: Rozvoj vědeckých kapacit Slezské univerzity v Opavě</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Topology Proceedings

ISSN

0146-4124

e-ISSN

—

Svazek periodika

52

Číslo periodika v rámci svazku

2018

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

205-218

Kód UT WoS článku

—

EID výsledku v databázi Scopus

—