Sharkovskii's Theorem Under Set-Valued Functions
Access rightsWorldwide access
MetadataShow full item record
Sharkovskii's remarkable theorem from 1964 demonstrated significant results about periodic orbits of continuous functions on the real line. His work produced the Sharkovskii ordering. If m >> n in the Sharkovskii ordering and if f has a periodic orbit of period m, it must also have a periodic orbit of period n. While Sharkovskii worked with classical continuous functions, this paper expands Sharkovskii's theorem to a class of set-valued functions. In particular, we show that the ordering holds for upper semicontinuous set-valued functions with the strong intermediate value property.