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 $\geq 2$.
Publié le : 2009-06-15
Classification:
Set of periods,
periodic points,
holomorphic maps,
homotopy,
Riemann surfaces,
55M20,
57N05,
57N10
@article{1246454033,
author = {Llibre, Jaume and Marzantowicz, Wac\l aw},
title = {Homotopy minimal periods of holomorphic maps on surfaces},
journal = {Funct. Approx. Comment. Math.},
volume = {40},
number = {1},
year = {2009},
pages = { 309-326},
language = {en},
url = {http://dml.mathdoc.fr/item/1246454033}
}
Llibre, Jaume; Marzantowicz, Wacław. Homotopy minimal periods of holomorphic maps on surfaces. Funct. Approx. Comment. Math., Tome 40 (2009) no. 1, pp. 309-326. http://gdmltest.u-ga.fr/item/1246454033/