Algebraic entropy and the space of initial values for discrete dynamical systems (Q2773082)
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: Algebraic entropy and the space of initial values for discrete dynamical systems |
scientific article; zbMATH DE number 1709236
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Algebraic entropy and the space of initial values for discrete dynamical systems |
scientific article; zbMATH DE number 1709236 |
Statements
Algebraic entropy and the space of initial values for discrete dynamical systems (English)
0 references
5 December 2002
0 references
algebraic entropy
0 references
rational map
0 references
invariant sublattices
0 references
discrete Painlevé equations
0 references
The author presents some basic formulae to calculate the degree of the \(n\)th iterate of the sequence of rational map. In the case where the maps are birational and have the space of initial values the calculation reduces to the calculation of the power of some matrix. The author also shows examples of calculation and simplifies the method by considering invariant sublattices. Moreover, this paper presents an application of the method developed here to discrete Painlevé equations and shows that for all of them the degrees grow at most in the order \(n^2\). The proof is based on the corresponding root systems.
0 references
