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Sbornik: Mathematics, 2019, Volume 210, Issue 12, Pages 1663–1689
DOI: https://doi.org/10.1070/SM9168 (Mi sm9168) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The action of the Monge-Ampère operator on polynomials in the plane and its fixed points of polynomial type

Yu. A. Aminov

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine
English version PDF (519 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM9168
Abstract: The action of the Monge-Ampère operator on polynomials of degree four in two variables is investigated. Two necessary conditions for the Monge-Ampère equation to have a solution are established. Sufficient conditions for solvability are indicated, which coincide with necessary conditions in certain cases. Invariant submanifolds of the action of the Monge-Ampère operator are found. Closed invariant chains of polynomials are constructed, and all the fixed points having the form of general polynomials of degree four are found.
Bibliography: 9 titles.
Keywords: cone, conic, necessary condition, solvability of equations, invariant set, fixed point.
Received: 12.09.2018 and 02.04.2019
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 12, Pages 3–30
DOI: https://doi.org/10.4213/sm9168
Bibliographic databases:
Document Type: Article
UDC: 514.77+517.95
MSC: 35C11, 35G20
Language: English
Original paper language: Russian
Citation: Yu. A. Aminov, “The action of the Monge-Ampère operator on polynomials in the plane and its fixed points of polynomial type”, Mat. Sb., 210:12 (2019), 3–30; Sb. Math., 210:12 (2019), 1663–1689
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:8
    References:28
    First page:15
     
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