Sharkovskiĭ's theorem holds for some discontinuous functions
Volume 179 / 2003
Fundamenta Mathematicae 179 (2003), 27-41
MSC: Primary 26A15; Secondary 26A18, 26A21, 54C30, 37E99.
DOI: 10.4064/fm179-1-3
Abstract
We show that the Sharkovski{ĭ} ordering of periods of a continuous real function is also valid for every function with connected $G_\delta $ graph. In particular, it is valid for every ${\rm DB}_1$ function and therefore for every derivative. As a tool we apply an Itinerary Lemma for functions with connected $G_\delta $ graph.
