On codimension one foliations with prescribed cuspidal separatrix
Percy Fern\'andez-S\'anchez, Jorge Mozo-Fern\'andez, Hern\'an, Neciosup

TL;DR
This paper develops a pre-normal form for certain codimension one holomorphic foliations with cuspidal separatrices and provides conditions for these foliations to be of generalized surface type in three dimensions.
Contribution
It introduces a pre-normal form for germs of foliations with cuspidal separatrices and establishes a sufficient condition for their classification as generalized surface type in three dimensions.
Findings
Constructed a pre-normal form for cuspidal separatrix foliations.
Provided a sufficient condition for generalized surface type classification.
Focused on quasi-homogeneous, three-dimensional cases.
Abstract
In this paper, we will construct a pre-normal form for germs of codimension one holomorphic foliation having a particular type of separatrix, of cuspidal type. We will also give a sufficient condition, in the quasi-homogeneous, three-dimensional case, for these foliations to be of generalized surface type.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory · Mathematical Dynamics and Fractals
