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- W2950600404 abstract "We consider planar vector field without zeroes X and study the image of the associated Lie derivative operator LX acting on the space of smooth functions. We show that the cokernel of LX is infinite-dimensional as soon as X is not topologically conjugate to a constant vector field and that, if the topology of the integral trajectories of X is ``simple enough'' (e.g. if X is polynomial) then X is transversal to a Hamiltonian foliation. We use this fact to find a large explicit subalgebra of the image of LX and to build an embedding of R^2 into R^4 which rectifies X. Finally we use this embedding to characterize the functions in the image of LX." @default.
- W2950600404 created "2019-06-27" @default.
- W2950600404 creator A5020874083 @default.
- W2950600404 date "2010-07-18" @default.
- W2950600404 modified "2023-09-27" @default.
- W2950600404 title "Solvability of the cohomological equation for regular vector fields on the plane" @default.
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