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Published in last 50 years
Let X be a metric space, f ∈ C0( X), andV ⊂X. The set-trajectory ( V, f( V), …,f n (V)) is investigated and some conditions for f to have periodic points with given periods are obtained.
A theorem of Block and Franke is improved on the existence of periodic points for a map of a circle to itself and a proof which seems more understandable is given.
Characterization of the rotation set and existence of periodic points of endomorphisms of a circle