The Monge Problem of “Piles and Holes” on the Torus and the Problem of Small Denominators
- Авторы: Kozlov V.1
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Учреждения:
- Steklov Institute of Mathematics
- Выпуск: Том 59, № 6 (2018)
- Страницы: 1090-1093
- Раздел: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172116
- DOI: https://doi.org/10.1134/S0037446618060113
- ID: 172116
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Аннотация
We discuss the problem of existence of a smooth endomorphism of a closed n-dimensional manifold carrying a differential n-form into a prescribed volume form. Of course, we assume that the integrals of these forms over the whole manifold are equal. The solution of this problem for the n-dimensional torus reduces to the problem of small denominators well known in analysis.
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Об авторах
V. Kozlov
Steklov Institute of Mathematics
Автор, ответственный за переписку.
Email: kozlov@pran.ru
Россия, Moscow