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A new approach to the Poincaré center problem
Isaac A. García, Jaume Giné
We address the classical (degenerate or non-degenerate) center problem posed by Poincaré in the 19th century for monodromic singularities of analytic families of planar vector fiel…
Monodromic singularities of Brunella-Miari vector fields with two edges in the Newton diagram
Isaac A. García, Jaume Giné, Víctor Mañosa
This work focuses on the study of monodromic singularities in planar analytic families of vector fields whose Newton diagram consists of exactly two edges. We begin by analyzing th…
Principal Bautin ideal of monodromic singularities with inverse integrating factors
Isaac A. García, Jaume Giné
We analyze the structure of the Poincaré map associated to a monodromic singularity of an analytic family of planar vector fields. We work under two assumptions. The first one…
Characterization of centers by its complex separatrices
Isaac A. García, Jaume Giné
In this work we deal with analytic families of real planar vector fields having a monodromic singularity at the origin for any and depe…