Geodesic
On Pawlak's problem concerning entropy of almost continuous functions
Tomasz Natkaniec 1   ; Piotr Szuca 2
1 Institute of Mathematics Gdańsk University Wita Stwosza 57 80-952 Gdańsk, Poland
2 Institute of Mathematics Gdańsk University Wita Stwosza 57 80–952 Gdańsk, Poland
Colloquium Mathematicum, Tome 121 (2010) no. 1, pp. 107-111 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $A$.
DOI : 10.4064/cm121-1-9
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

Tomasz Natkaniec  1   ; Piotr Szuca  2

1 Institute of Mathematics Gdańsk University Wita Stwosza 57 80-952 Gdańsk, Poland
2 Institute of Mathematics Gdańsk University Wita Stwosza 57 80–952 Gdańsk, Poland 
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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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