On Pawlak's problem concerning entropy of almost continuous functions

• Autorzy: Tomasz Natkaniec , Piotr Szuca
• Języki publikacji: EN

Abstrakty

EN

We prove that if f:𝕀 → 𝕀 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:𝕀 → 𝕀 with positive entropy for which the set Per(f) of prime periods of all periodic points is equal to A.

Kategorie tematyczne

• 37B40: Topological entropy
• 26A18: Iteration
• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 121
• Numer: 1
• Strony: 107-111

Daty

wydano

2010

Twórcy

autor

Tomasz Natkaniec

• Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland

autor

Piotr Szuca

• Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/cm121-1-9