Abstract.
We give an elementary proof that, in its domain of definition, the time-p map of a scalar, autonomous holomorphic, complex differential equation, is itself holomorphic. This result is used by Sverdlove [1] when considering limit cycles in complex holomorphic differential equations. However no proof or reference for the result is given in [1]. Although this result must be well established, a proof does not appear to be readily accessible in the reference literature.
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Needham, D.J. Holomorphic complex differential equations: An elementary proof that the time-p map is holomorphic. Z. angew. Math. Phys. 57, 1092–1095 (2006). https://doi.org/10.1007/s00033-006-0082-5
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DOI: https://doi.org/10.1007/s00033-006-0082-5