Analytic integrability of some examples of degenerate planar vector fields
MetadataShow full item record
This paper is devoted to the classification of analytic integrable cases of two families of degenerate planar vector fields with a monodromic singular point at the origin. This study falls in the still open degenerate center problem. This classification can be done using the formal normal form theory and knowing a suitable normal form of any differential systems associated to each family.
Is part ofActa Applicandae Mathematicae, 2016, vol. 141, p. 1-15
European research projects
Showing items related by title, author, creator and subject.
Algaba, Antonio; Díaz, María; García, Cristóbal; Giné, Jaume (Elsevier, 2022)We generalize the method of construction of an integrating factor for Abel differential equations, developed in Briskin et al. (1998), for any generic monodromic singularity. Here generic means that the vector field has ...
Giné, Jaume; Algaba, Antonio; García, Cristóbal (Hindawi Publishing Corporation, 2013)We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results ...
Algaba, Antonio; García, Cristóbal; Giné, Jaume (MDPI, 2021)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 reversibility and conjugate reversibility ...