# zbMATH — the first resource for mathematics

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.

##### MSC:
 37B99 Topological dynamics 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
Full Text:
##### References:
 [1] DOI: 10.1007/BF01408935 · Zbl 0425.58016 [2] Yoccoz, C.R.A.S. 298 pp none– (1984) [3] Poincaré, Oeuvres Complètes pp 137– (1952) [4] DOI: 10.1007/BF02760466 · Zbl 0442.54011 [5] Hall, Ergod. Th. & Dynam. Sys. 1 pp 261– (1981) [6] Denjoy, J. Math. Pures Appl. 11 pp 333– (1932) [7] DOI: 10.1007/BF01425575 · Zbl 0272.58005 [8] Nitecki, Differentiable Dynamics: An Introduction to the Orbit Structure of Diffeomorphisms (1971) · Zbl 0246.58012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.