Email this article The action of the Monge-Ampère operator on polynomials in the plane and its fixed points of polynomial type
- Authors: Aminov Y.A.1
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Affiliations:
- B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
- Issue: Vol 210, No 12 (2019)
- Pages: 3-30
- Section: Articles
- URL: https://bakhtiniada.ru/0368-8666/article/view/133294
- DOI: https://doi.org/10.4213/sm9168
- ID: 133294
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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.
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About the authors
Yuriy Akhmetovich 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
References
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