Definition of "holomorphic"

The iteration of holomorphic maps of one variable is one of the most lively fields of current mathematical research. Since its beginning in the twenties of this century, the theory of holomorphic endomorphisms of the Riemann sphere (= rational functions) has become well developed.

1998, Stefan-M. Heinemann, Julia Sets in Cn, Hartje Kriete, Progress in Holomorphic Dynamics, Addison Wesley Longman, page 159

A holomorphic 1-form on X is closed, and so 0 = d η 1 = d f ∧ η 2 {\displaystyle 0=d\eta _{1}=df\land \eta _{2}} .

1998, Robert Friedman, Algebraic Surfaces and Holomorphic Vector Bundles, Springer, page 303

The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector field) acting on it.

2010, Graziano Gentili, Jacques Guenot, Giorgio Patrizio, Holomorphic Dynamical Systems: Lectures given at the C.I.M.E. Summer School, Springer, page v