42522

Автор(ы): 

Автор(ов): 

2

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

On Lie problem and differential invariants for the subgroup of the plane Cremona group

DOI: 

10.1016/j.geomphys.2017.06.007

Наименование источника: 

  • Journal of Geometry and Physics

Обозначение и номер тома: 

Volume 121

Город: 

  • Amsterdam

Издательство: 

  • Elsevier B.V.

Год издания: 

2017

Страницы: 

72-82
Аннотация
We develop a new approach to the study of subgroups in the Cremona group. Namely, we consider the class of differential equations $y''=F(x,y)$ with rational right parts and its symmetry group. This group is a subgroup in the Cremona group of birational automorphisms of $\mathbb{C}^2$, which makes it possible to apply for their study methods of differential invariants and geometric theory of differential equations. Also, using algebraic methods in the theory of differential equations we obtain a global classification for such equations instead of local classifications for such problems provided by Lie, Tresse and others.

Библиографическая ссылка: 

Малахов А.И., Бибиков П.В. On Lie problem and differential invariants for the subgroup of the plane Cremona group // Journal of Geometry and Physics. 2017. Volume 121. С. 72-82.

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