This article is cited in 1 paper

On one class of regular $\lambda$-truncations and its applications to inverse functions

A. V. Arutyunov, S. E. Zhukovskiy

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow

Abstract: One class of polynomial mappings is studied. Any mapping in this class is shown to be a $\lambda$-truncation for some vector $\lambda$. In addition, for each mapping in this class there exists a direction along which this mapping is regular. It is shown that if some infinitely differentiable mapping is representable near the origin as the sum of the mapping under consideration and a perturbation (small in some sense), then this mapping has a continuous inverse function in some neighborhood of the origin.

Keywords: polynomial mapping, $\lambda$-truncation, regular direction, inverse function.

UDC: 517.275

MSC: 26B10

Received: 23.04.2024
Revised: 18.11.2024

DOI: 10.4213/mzm14353

 English version: Mathematical Notes, 2025, 117:5, 693–706

Bibliographic databases:

•