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Mat. Sb., 2016, Volume 207, Number 9, Pages 3–34 (Mi msb8611)  

This article is cited in 3 scientific papers (total in 3 papers)

Properties of surjective real quadratic maps

A. V. Arutyunovabc, S. E. Zhukovskiya

a Peoples Friendship University of Russia, Moscow
b Lomonosov Moscow State University
c Tambov State University

Abstract: The properties of surjective real quadratic maps are investigated. Sufficient conditions for the property of surjectivity to be stable under various perturbations are obtained. Examples of surjective quadratic maps whose surjectivity breaks down after an arbitrarily small perturbation are constructed. Sufficient conditions for quadratic maps to have nontrivial zeros are obtained. For a smooth even map in a neighbourhood of the origin an inverse function theorem in terms of the degree of the corresponding quadratic map is obtained. A canonical form of surjective quadratic maps from $\mathbb{R}^3$ to $\mathbb{R}^3$ is constructed.
Bibliography: 27 titles.

Keywords: quadratic map, inverse function, nontrivial zero.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.333.2014/K
НШ-8215.2016.1
Russian Foundation for Basic Research 15-01-04601-а
16-01-00677-а
Russian Science Foundation 15-11-10021
This work was supported by the Ministry of Education and Science of the Russian Federation (project no. 1.333.2014/K), the Russian Foundation for Basic Research (grant nos. 15-01-04601-a and 16-01-00677-a) and the Programme of the President of the Russian Federation for the Support of Leading Scientific Schools (grant no. НШ-8215.2016.1). The results in § \ref{s6} are due to A. V. Arutyunov, who was supported by a grant from the Russian Science Foundation (project no. 15-11-10021).


DOI: https://doi.org/10.4213/sm8611

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English version:
Sbornik: Mathematics, 2016, 207:9, 1187–1214

Bibliographic databases:

Document Type: Article
UDC: 517.275+515.164.15
MSC: Primary 15A63; Secondary 90C20
Received: 06.10.2015 and 25.02.2016

Citation: A. V. Arutyunov, S. E. Zhukovskiy, “Properties of surjective real quadratic maps”, Mat. Sb., 207:9 (2016), 3–34; Sb. Math., 207:9 (2016), 1187–1214

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. V. Arutyunov, S. E. Zhukovskiy, D. Yu. Karamzin, “Some properties of two-dimensional surjective $p$-homogeneous maps”, Comput. Math. Math. Phys., 57:7 (2017), 1081–1089  mathnet  crossref  crossref  mathscinet  isi  elib
    2. I. Karzhemanov, I. Zhdanovskiy, “Some properties of surjective rational maps”, Eur. J. Math., 4:1 (2018), 326–329  crossref  mathscinet  zmath  isi  scopus
    3. A. V. Arutyunov, “IInvestigation of the sets of real solutions of non-linear equations”, Izv. Math., 83:2 (2019), 199–213  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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