46755

Автор(ы): 

Автор(ов): 

2

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

ON CLASSIFICATION PROBLEMS IN THE THEORY OF DIFFERENTIAL EQUATIONS: ALGEBRA + GEOMETRY

Наименование источника: 

  • Publications de l'Institut Mathematique

Обозначение и номер тома: 

Т.103, вып. 117

Город: 

  • Belgrade

Издательство: 

  • Mathematical Institute of the Serbian Academy of Sciences and Arts

Год издания: 

2018

Страницы: 

1-20
Аннотация
We study geometric and algebraic approaches to classi cation problems of differential equations. We consider the so-called Lie problem: provide the point classi cation of ODEs y′′ = F(x; y). In the rst part of the paper we consider the case of smooth right-hand side F. The symmetry group for such equations has in nite dimension, so classical constructions from the theory of differential invariants do not work. Nevertheless, we compute the algebra of differential invariants and obtain a criterion for the local equiva- lence of two ODEs y′′ = F(x; y). In the second part of the paper we develop a new approach to the study of subgroups in the Cremona group. Namely, we consider class of differential equations y′′ = F(x; y) with rational right hand sides and its symmetry group. This group is a subgroup in the Cremona group of birational automorphisms of C2, which makes it possible to apply for their study methods of differential invariants and geometric theory of differ- ential equations. Also, using algebraic methods in the theory of differential equations we obtain a global classi cation for such equations instead of local classi cations for such problems provided by Lie, Tresse and others.

Библиографическая ссылка: 

Бибиков П.В., Малахов А.И. ON CLASSIFICATION PROBLEMS IN THE THEORY OF DIFFERENTIAL EQUATIONS: ALGEBRA + GEOMETRY // Publications de l'Institut Mathematique. 2018. Т.103, вып. 117. С. 1-20.