A generalized definition of topological entropy

@article{30529,
   author = {Rucká, Lenka and Block, Louis and Keesling, James},
   article_location = {Auburn},
   article_number = {2018},
   keywords = {minimal set; topological entropy},
   language = {eng},
   issn = {0146-4124},
   journal = {Topology Proceedings},
   title = {A generalized definition of topological entropy},
   url = {http://topology.auburn.edu/tp/reprints/v52/},
   volume = {52},
   year = {2018}
}

TY  - JOUR
ID  - 30529
AU  - Rucká, Lenka - Block, Louis - Keesling, James
PY  - 2018
TI  - A generalized definition of topological entropy
JF  - Topology Proceedings
VL  - 52
IS  - 2018
SP  - 205-218
EP  - 205-218
PB  - Auburn University
SN  - 01464124
KW  - minimal set
KW  - topological entropy
UR  - http://topology.auburn.edu/tp/reprints/v52/
L2  - http://topology.auburn.edu/tp/reprints/v52/
N2  - 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.
ER  - 

RUCKÁ, Lenka, Louis BLOCK and James KEESLING. A generalized definition of topological entropy. \textit{Topology Proceedings}. Auburn: Auburn University, 2018, vol.~52, No~2018, p.~205-218. ISSN~0146-4124.