Minimal periods of holomorphic maps on complex tori

Abstract

We study the set of minimal periods of holomorphic self-maps of one- and two-dimensional complex tori. In particular, we characterize when the set of minimal periods of such maps is finite. In fact, we have an algorithm for doing this characterization for holomorphic self-maps of an arbitrary dimensional complex torus.

Keywords:

• set of minimal periods
• periodic points
• holomorphic maps on complex tori

2000 Mathematics Subject Classification::

• Primary 37C25
• Secondary 32H50

View correction statement:

Corrigendum to “Minimal periods of holomorphic maps on complex tori” [J. Differ. Equ. Appl. 18 (2012) 2059–2068]

Acknowledgements

The first author is partially supported by a MICIIN/FEDER grant number MTM 2008-03437, by an AGAUR grant number 2009SGR 410 and by ICREA Academia. The second author is partially supported by grant 11001172 from the National Natural Science Foundation of China and grant 20100073120067 from Research Fund for the Doctoral Program of Higher Education of China.