On Pawlak's problem concerning entropy of almost continuous functions
Tomasz Natkaniec ; Piotr Szuca
Colloquium Mathematicae, Tome 120 (2010), p. 107-111 / Harvested from The Polish Digital Mathematics Library
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We prove that if f: → is Darboux and has a point of prime period different from 2i, 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.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:283956 
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Tomasz Natkaniec; Piotr Szuca. On Pawlak's problem concerning entropy of almost continuous functions. Colloquium Mathematicae, Tome 120 (2010) pp. 107-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm121-1-9/