© Wydawnictwo Naukowe UAM, Poznań 2009. In this paper we study the minimal periods on a holomorphic map which are preserved by any of its deformation considering separately the case of continuous and holomorphic homotopy. A complete description of the set of such minimal periods for holomorphic self-map of a compact Riemann surface is given. It shows that a nature of answer depends on the geometry of the surface distinguishing the parabolic case of the Riemann sphere, elliptic case of tori and the hyperbolic case of a surface of genus ≤ 2.
|Journal||Functiones et Approximatio, Commentarii Mathematici|
|Publication status||Published - 1 Jan 2009|
- Holomorphic maps
- Periodic points
- Riemann surfaces
- Set of periods