Automatic differentiability and characterization of cocycles of holomorphic flows

Farhad Jafari, Thomas Tonev, Elena Toneva

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

In this paper we prove that cocycles of holomorphic flows on do-mains 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.

Original languageEnglish (US)
Pages (from-to)3389-3394
Number of pages6
JournalProceedings of the American Mathematical Society
Volume133
Issue number11
DOIs
StatePublished - Nov 2005

Keywords

  • Cocycle
  • Flow
  • Infinitesimal generator

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