The topological entropy versus level sets for interval maps (part II)

• Autorzy: Jozef Bobok
• Języki publikacji: EN

Abstrakty

EN

Let f: [a,b] → [a,b] be a continuous function of the compact real interval such that (i) $card f^{-1}(y) ≥ 2$ for every y ∈ [a,b]; (ii) for some m ∈ {∞,2,3,...} there is a countable set L ⊂ [a,b] such that $card f^{-1}(y) ≥ m$ for every y ∈ [a,b]∖L. We show that the topological entropy of f is greater than or equal to log m. This generalizes our previous result for m = 2.

Kategorie tematyczne

• 37B40: Topological entropy
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 166
• Numer: 1
• Strony: 11-27

Daty

wydano

2005

Twórcy

autor

Jozef Bobok

• KM FSv ČVUT, Thákurova 7, 166 29 Praha 6, Czech Republic

Identyfikatory

DOI

10.4064/sm166-1-2