On Denjoy’s theorem for endomorphisms. (English) Zbl 0657.58018

In this paper we give an extension to \(C^ 2\)-endomorphisms of the circle of the well known Denjoy’s theorem on \(C^ 2\)-diffeomorphisms. We also give a simple proof of an extension of Block and Franke’s theorem on the existence of periodic points for maps of the circle.


37B99 Topological dynamics
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
Full Text: DOI


[1] DOI: 10.1007/BF01408935 · Zbl 0425.58016
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