On Pawlak's problem concerning entropy of almost continuous
functions
Colloquium Mathematicum, Tome 121 (2010) no. 1, pp. 107-111
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove that if $f:{\mathbb I}\to{\mathbb I}$ is Darboux and has a point of
prime period different from $2^i$, $i=0,1,\ldots,$ then the entropy
of $f$ is positive. On the other hand, for every set
$A\subset{\mathbb N}$ with $1\in A$ there is an almost continuous (in the
sense of Stallings) function $f:{\mathbb I}\to{\mathbb I}$ with positive
entropy for which the set $\mathop{\rm Per}(f)$ of prime periods of all periodic
points is equal to $A$.
Keywords:
prove mathbb mathbb darboux has point prime period different ldots entropy positive other every set subset mathbb there almost continuous sense stallings function mathbb mathbb positive entropy which set mathop per prime periods periodic points equal
Affiliations des auteurs :
Tomasz Natkaniec 1 ; Piotr Szuca 2
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author = {Tomasz Natkaniec and Piotr Szuca},
title = {On {Pawlak's} problem concerning entropy of almost continuous
functions},
journal = {Colloquium Mathematicum},
pages = {107--111},
publisher = {mathdoc},
volume = {121},
number = {1},
year = {2010},
doi = {10.4064/cm121-1-9},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm121-1-9/}
}
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Tomasz Natkaniec; Piotr Szuca. On Pawlak's problem concerning entropy of almost continuous functions. Colloquium Mathematicum, Tome 121 (2010) no. 1, pp. 107-111. doi: 10.4064/cm121-1-9
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