This article is cited in 25 papers

The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping

E. R. Avakov, A. A. Agrachev, A. V. Arutyunov


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 $F$.

UDC: 517.9

MSC: 58C25

Received: 01.08.1990

 English version: Mathematics of the USSR-Sbornik, 1992, 73:2, 455–466

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