电邮这篇文章 The action of the Monge-Ampère operator on polynomials in the plane and its fixed points of polynomial type
- 作者: Aminov Y.A.1
-
隶属关系:
- B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
- 期: 卷 210, 编号 12 (2019)
- 页面: 3-30
- 栏目: Articles
- URL: https://bakhtiniada.ru/0368-8666/article/view/133294
- DOI: https://doi.org/10.4213/sm9168
- ID: 133294
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详细
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.
作者简介
Yuriy Aminov
B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
Email: aminov@ilt.kharkov.ua
Doctor of physico-mathematical sciences, Professor
参考
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- Ю. А. Аминов, “О полиномиальных решениях уравнения Монжа–Ампера”, Матем. сб., 205:11 (2014), 3–38
- Yu. Aminov, K. Arslan, B. Bayram, B. Bulca, C. Murathan, G. Öztürk, “On the solution of the Monge–Ampère equation $Z_{xx}Z_{yy}-Z_{xy}^2=f(x,y)$ with quadratic right side”, Журн. матем. физ., анал., геом., 7:3 (2011), 203–211
- И. Х. Сабитов, “Глобальные решения тривиального уравнения Монжа–Ампера с изолированными особенностями”, Тезисы докладов международной конференции “Геометрия в Одессе – 2015”, Одесса, 2015, 86
- И. Х. Сабитов, “Решение тривиального уравнения Монжа–Ампера с изолированными особыми точками”, Сиб. электрон. матем. изв., 13 (2016), 740–743
- J. A. Galvez, B. Nelli, “Entire solutions of the degenerate Monge–Ampère equation with a finite number of singularities”, J. Differential Equations, 261:11 (2016), 6614–6631
- В. И. Фущич, В. М. Штелень, Н. И. Серов, Симметрийный анализ и точные решения нелинейных уравнений математической физики, Наукова думка, Киев, 1989, 336 с.
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