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

Jozef Bobok. "The topological entropy versus level sets for interval maps (part II)." Studia Mathematica 166.1 (2005): 11-27. <http://eudml.org/doc/284616>.

@article{JozefBobok2005,
abstract = {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.},
author = {Jozef Bobok},
journal = {Studia Mathematica},
keywords = {interval map; level set; topological entropy},
language = {eng},
number = {1},
pages = {11-27},
title = {The topological entropy versus level sets for interval maps (part II)},
url = {http://eudml.org/doc/284616},
volume = {166},
year = {2005},
}

TY - JOUR
AU - Jozef Bobok
TI - The topological entropy versus level sets for interval maps (part II)
JO - Studia Mathematica
PY - 2005
VL - 166
IS - 1
SP - 11
EP - 27
AB - 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.
LA - eng
KW - interval map; level set; topological entropy
UR - http://eudml.org/doc/284616
ER -