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

This article refers to:

Minimal periods of holomorphic maps on complex tori

In [1] we studied the minimal periods of holomorphic maps on complex tori. In particular, we gave complete answers in dimensions one and two and outlined an algorithm for higher dimensions. However, due to two simple calculation mistakes in the proof of [1, Theorem 4], there were two subcases omitted in its statement.

On [1, p. 2064], in the case p = 2 and q = 1, we should have . Then is periodic as . Thus , which belongs to case (F4).

On [1, p. 2065], in the case and q = 1, we should have . Then N(f ^m ) = 9 for all . Thus , which belongs to case (F1).

Therefore, the correct statement for miminal periods of holomorphic maps on two-dimensional complex tori should be as follows.

Theorem 1

Let be a holomorphic map, and let , , and be the eigenvalues of . Then Per is equal to

	(E) ∅ if and only if
	(F1) if and only if is either , or , or , or , or , or , or , or
	(F2) if and only if is either , or , or
	(F3) if and only if
	(F4) if and only if is either , or , or , or
	(F5) if and only if
	(F6) if and only if
	(F7) if and only if
	(G) infinite otherwise.

Additional information

Notes on contributors

Feng Rong

1

Notes

1. [email protected]