On pairs of regular foliations in \({\mathbb{R}^3}\) and singularities of map-germs
The authors study germs at the origin of pairs of codimension one regular foliations in the 3-dimensional Euclidean space. The smooth classification is treated and it is related to the classification of certain divergent diagrams. The paper is organized as follows. In Section 2, some preliminaries and concepts from singularity theory are given. In Section 3, the classification of regular foliations up to formal equivalence is studied, and in Section 4, a complete topological classification is given. Section 5 deals with various classifications of the singularities of the discriminant. Other papers of the authors connected to this subject are [\textit{R. D. S. Oliveira} and \textit{F. Tari}, Hokkaido Math. J. 31, No.~3, 523--537 (2002; Zbl 1036.34045) and \textit{F. Tari}, Discrete Contin. Dyn. Syst. 13, No.~1, 139--162 (2005; Zbl 1081.34007)].
scientific article; zbMATH DE number 5306125