On Pawlak's problem concerning entropy of almost continuous functions

Tomasz Natkaniec, and Piotr Szuca. "On Pawlak's problem concerning entropy of almost continuous functions." Colloquium Mathematicae 121.1 (2010): 107-111. <http://eudml.org/doc/283956>.

@article{TomaszNatkaniec2010,
abstract = {We prove that if f: → is Darboux and has a point of prime period different from $2^i$, i = 0,1,..., then the entropy of f is positive. On the other hand, for every set A ⊂ ℕ with 1 ∈ A there is an almost continuous (in the sense of Stallings) function f: → with positive entropy for which the set Per(f) of prime periods of all periodic points is equal to A.},
author = {Tomasz Natkaniec, Piotr Szuca},
journal = {Colloquium Mathematicae},
language = {eng},
number = {1},
pages = {107-111},
title = {On Pawlak's problem concerning entropy of almost continuous functions},
url = {http://eudml.org/doc/283956},
volume = {121},
year = {2010},
}

TY - JOUR
AU - Tomasz Natkaniec
AU - Piotr Szuca
TI - On Pawlak's problem concerning entropy of almost continuous functions
JO - Colloquium Mathematicae
PY - 2010
VL - 121
IS - 1
SP - 107
EP - 111
AB - We prove that if f: → is Darboux and has a point of prime period different from $2^i$, i = 0,1,..., then the entropy of f is positive. On the other hand, for every set A ⊂ ℕ with 1 ∈ A there is an almost continuous (in the sense of Stallings) function f: → with positive entropy for which the set Per(f) of prime periods of all periodic points is equal to A.
LA - eng
UR - http://eudml.org/doc/283956
ER -