Abstract
AbstractIn this work, we present some criteria about the existence and nonexistence of both Puiseux inverse integrating factors and Puiseux first integrals for planar analytic vector fields having a monodromic singularity. These functions are a wide generalization of their formal or algebraic counterpart in Cartesian coordinates . We prove that none of the functions and can be used to characterize degenerate centers although the existence of is a sufficient center condition.
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