E. R. Avakov, A. A. Agrachev, A. V. Arutyunov, The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping

Title: The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping
Authors: E. R. Avakov, A. A. Agrachev, A. V. Arutyunov
Journal title: Math. USSR-Sb.
Year: 1992
Issue: 2
Volume: 73
Pages: 455-466
Citation:

E. R. Avakov, A. A. Agrachev, A. V. Arutyunov, “The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping”, Mathematics of the USSR-Sbornik, 1992, 73:2, 455–466

Abstract:

The level set $$M$$ of a smooth mapping $$F$$ in a neighborhood of an anormal point is investigated. Concepts of 2-regularity are introduced for it. It is proved that if the mapping is 2-regular at the point under consideration, then in a neighborhood of it the set $$M$$ is locally diffeomorphic to the set of zeros of the second differential of $$F$$.