In this work we deal with analytic families of real planar vector fields $\mathcal {X} _\lambda
$ having a monodromic singularity at the origin for any $\lambda\in\Lambda\subset\mathbb …

We analyze the structure of the Poincar\'e map $\Pi $ associated to a monodromic singularity
of an analytic family of planar vector fields. We work under two assumptions. The first one is …

We consider the two-dimensional autonomous systems of differential equations where the
origin is a monodromic degenerate singular point, ie, with null linear part. In this work we …

In this work, we present some criteria about the existence and nonexistence of both Puiseux
inverse integrating factors VV and Puiseux first integrals HH for planar analytic vector fields …

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We consider analytic families of planar vector fields depending analytically on the
parameters in Λ that guarantee the existence of a (may be degenerate and with …

For perturbations of integrable non-Hamiltonian quasi-homogeneous planar vector field
whose origin is a non-degenerate singular point, orbital linearization and analytic …

In this work we use the normal form theory to establish an algorithm to determine if a planar
vector field is orbitally reversible. In previous works only algorithms to determine the …

In this paper we study the analytic integrability around the origin inside a family of
degenerate centers or perturbations of them. For this family analytic integrability does not …

We consider the center-focus problem for analytic families of planar vector fields having a
monodromic singularity with characteristic directions. We give a method to compute the …