Singularities of 3d vector fields preserving the form of Martinet

2022/11/07 by Stavros Anastassiou, Anastassiou, Stavros
Mathematics · Physics and Astronomy · Engineering · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Control and Dynamics of Mobile Robots

paper · pdf · doi:10.48550/arxiv.2211.03619

Abstract

We study the local structure of vector fields on ℝ³ which preserve the Martinet 1-form α=(1+x)dy± zdz. We present the classification of their singularities, up to diffeomorphisms preserving the form α, as well as their transversal unfoldings. We are thus able to provide a fairly complete list of the bifurcations such vector fields undergo.

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