Geodesic
The action of the Monge-Amp\`ere operator on polynomials in the plane and its fixed points of polynomial type
Sbornik. Mathematics, Tome 210 (2019) no. 12, pp. 1663-1689

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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, fixed point.
Mots-clés : invariant set 
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     title = {The action of the {Monge-Amp\`ere} operator on polynomials in the plane and its fixed points of polynomial type},
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Yu. A. Aminov. The action of the Monge-Amp\`ere operator on polynomials in the plane and its fixed points of polynomial type. Sbornik. Mathematics, Tome 210 (2019) no. 12, pp. 1663-1689. http://geodesic.mathdoc.fr/item/SM_2019_210_12_a0/