Automatic differentiability and characterization of cocycles of holomorphic flows

Farhad Jafari, Thomas Tonev, Elena Toneva
2005 Proceedings of the American Mathematical Society  
In this paper we prove that cocycles of holomorphic flows on domains in the complex plane are automatically differentiable with respect to the flow parameter, and their derivatives are holomorphic functions. We use this result to show that, on simply connected domains, an additive cocycle is a coboundary if and only if this cocycle vanishes at the fixed point of the flow.
doi:10.1090/s0002-9939-05-07904-9 fatcat:b4b5g5kx3jdwljxzmagdjk3ce4