Sharkovskiĭ's theorem holds for some discontinuous functions

Piotr Szuca. "Sharkovskiĭ's theorem holds for some discontinuous functions." Fundamenta Mathematicae 179.1 (2003): 27-41. <http://eudml.org/doc/283126>.

@article{PiotrSzuca2003,
abstract = {We show that the Sharkovskiĭ ordering of periods of a continuous real function is also valid for every function with connected $G_δ$ graph. In particular, it is valid for every DB₁ function and therefore for every derivative. As a tool we apply an Itinerary Lemma for functions with connected $G_δ$ graph.},
author = {Piotr Szuca},
journal = {Fundamenta Mathematicae},
keywords = {periodic points; iteration; itinerary lemma; Sharkovskij's ordering; connectivity functions; Darboux Baire 1 functions, derivatives},
language = {eng},
number = {1},
pages = {27-41},
title = {Sharkovskiĭ's theorem holds for some discontinuous functions},
url = {http://eudml.org/doc/283126},
volume = {179},
year = {2003},
}

TY - JOUR
AU - Piotr Szuca
TI - Sharkovskiĭ's theorem holds for some discontinuous functions
JO - Fundamenta Mathematicae
PY - 2003
VL - 179
IS - 1
SP - 27
EP - 41
AB - We show that the Sharkovskiĭ ordering of periods of a continuous real function is also valid for every function with connected $G_δ$ graph. In particular, it is valid for every DB₁ function and therefore for every derivative. As a tool we apply an Itinerary Lemma for functions with connected $G_δ$ graph.
LA - eng
KW - periodic points; iteration; itinerary lemma; Sharkovskij's ordering; connectivity functions; Darboux Baire 1 functions, derivatives
UR - http://eudml.org/doc/283126
ER -