TL;DR
This paper explores singular 2-webs formed by two foliations in the plane, focusing on their tangent points, the polar curve, and the relationship between contact order and singularities.
Contribution
It introduces the concept of singular 2-webs with tangent points, defines the polar curve, and analyzes the link between contact order and singularities.
Findings
Polar curve characterizes tangent points of foliations.
Contact order influences the singularities of the polar curve.
Singular 2-webs generalize regular 2-webs with tangent points.
Abstract
A 2-web in the plane is given by two everywhere transverse 1-foliations. In this paper we introduce the study of singular 2-webs, given by any two foliations, which may be tangent in some points. We show that such two foliations are tangent along a curve, which will be called the polar curve of the 2-web, and we study the relationship between the contact order of leaves of both foliations and the singularities of the polar curve.
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Taxonomy
TopicsLiterature, Culture, and Criticism · Plant Surface Properties and Treatments · Vibration and Dynamic Analysis