Electronic Version 18 (1993), 19-31

Stewart Baldwin

If T is a tree, and f: T --> T is a continuous function having an orbit of size 3 contained in an arc, then a variation of Sharkovskii's Theorem gives points of all periods for f. However, it is possible that no orbit of size 4 is contained in an arc. In this paper, we study what happens to Sharkovskii's Theorem when periodic orbits of [0,1] or \Bbb R are replaced by periodic orbits of a tree (or a dendrite) in which the orbit is contained in an arc.

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volume 18: table of contents
topology proceedings Electronic Version