Shuffle and Faà di Bruno Hopf algebras in the center problem for ordinary differential equations (Q316700)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Shuffle and Faà di Bruno Hopf algebras in the center problem for ordinary differential equations |
scientific article; zbMATH DE number 6630136
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Shuffle and Faà di Bruno Hopf algebras in the center problem for ordinary differential equations |
scientific article; zbMATH DE number 6630136 |
Statements
Shuffle and Faà di Bruno Hopf algebras in the center problem for ordinary differential equations (English)
0 references
27 September 2016
0 references
shuffle Hopf algebra
0 references
center problem
0 references
first return map
0 references
Bell polynomial
0 references
0 references
Consider the differential equation NEWLINE\[NEWLINE\frac{dv}{dx}= \sum_{i=1}^{\infty} a_{i}(x)\, v^{i+1}. NEWLINE\]NEWLINE The center problem asks whether every solution \(v\) with a sufficiently small initial value satisfies \(v(T)=v(0)\) for a fixed positive real number \(T\). In this paper, the author describes the Hopf algebra approach to the center problem. Some combinatorial properties of the first return map are also studied.
0 references
