Evolution of the Sharkovsky theorem (Q6585751)

The well-known \textit{A. N. Sharkovskiĭ}'s theorem [Ukr. Mat. Zh. 16, 61--71 (1964; Zbl 0122.17504)] describes the coexistence of periods of periodic orbits of continuous maps of an interval to itself. The aim of this paper is to give a brief description of the Sharkovskiĭ's theorem and some results that evolved from this theorem, including a similar result for continuous maps of the circle to itself, some results for continuous maps of trees into themselves, and refinements of the Sharkovskiĭ's theorem for interval maps.