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Cohomological equation for a $\lambda -$resonant vector field



Toussaint SOHOU and Guehi MAMADOU
Université Félix HOUPHOUET BOIGNY Abidjan-Cocody
UFR de Mathématiques et Informatique
Labo de Maths Fondamentales
22 BP 582 ABIDJAN 22 CÔTE D'IVOIRE




Mathematics Subject Classification: [2000] : Primary 53C10, 15A15; Secondary 37A05, 37C10, 34M45
Keywords: Cohomological equation. $\lambda -$resonant vector field.

Abstract:

In this paper, we investigate the resolution of the continuous cohomological equation $L_{X}f=g $ where $X$ is a vector field on a manifold $M$ and $g$ a function on $M,$ both given. We solve this equation when $X$ is a diagonal $\lambda -$resonant vector field or a monomial $\lambda -$resonant vector field.

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