A generalized definition of topological entropy

Result code in 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>
Result on the web
<a href="http://topology.auburn.edu/tp/reprints/v52/" target="_blank" >http://topology.auburn.edu/tp/reprints/v52/</a>
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
A generalized definition of topological entropy
Original language description
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.
Czech name
—
Czech description
—

Project
<a href="/en/project/EE2.3.30.0007" target="_blank" >EE2.3.30.0007: Development of Research Capacities of the Silesian University in Opava</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)