@article{García2025, 
author = {Isaac A. García and Jaume Giné},
title = {Monodromic singularities without curves of zero angular speed},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {1},
pages = {1488-1500},
keywords = {periodic orbits, Poincaré map, center, invariant curve},
url = {https://www.sciopen.com/article/10.3934/math.2025069},
doi = {10.3934/math.2025069},
abstract = {We consider planar analytic vector fields        X   having a monodromic singular point with Poincaré map    Π. We use the fact that there always exists a real analytic invariant curve    F  =  0 of        X   in a neighborhood of that singularity. We find some relations between    Π and    F that can be used to determine new conditions that guarantee the analyticity of    Π at the singularity. In the special case that    F becomes an inverse integrating factor of        X  , we rediscover formulas obtained previously by other methods. Applications to the center-focus problem and also to vector fields with degenerate infinity are given.}
}