Automatic differentiability and characterization of cocycles of holomorphic flows
Copyright policy )Automatic differentiability and characterization of cocycles of holomorphic flows
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.
- Colorado School of Mines United States
- University of Colorado Anschutz Medical Campus United States
- University of Colorado Health United States
- University of Colorado Colorado Springs United States
- Colorado State University Pueblo United States
Groups and semigroups of linear operators, cocycle, infinitesimal generator, flow, Linear operators on function spaces (general), holomorphic flow, Smooth dynamical systems: general theory, General theory of univalent and multivalent functions of one complex variable, Dynamical aspects of holomorphic foliations and vector fields, Mathematics
Groups and semigroups of linear operators, cocycle, infinitesimal generator, flow, Linear operators on function spaces (general), holomorphic flow, Smooth dynamical systems: general theory, General theory of univalent and multivalent functions of one complex variable, Dynamical aspects of holomorphic foliations and vector fields, Mathematics
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