Algebraic entropy and the space of initial values for discrete dynamical systems
Exactly Solvable and Integrable Systems
2009-11-07 v2
Abstract
A method to calculate the algebraic entropy of a mapping which can be lifted to an isomorphism of a suitable rational surfaces (the space of initial values) are presented. It is shown that the degree of the th iterate of such a mapping is given by its action on the Picard group of the space of initial values. It is also shown that the degree of the th iterate of every Painlev\'e equation in sakai's list is at most and therefore its algebraic entropy is zero.
Cite
@article{arxiv.nlin/0103011,
title = {Algebraic entropy and the space of initial values for discrete dynamical systems},
author = {Tomoyuki Takenawa},
journal= {arXiv preprint arXiv:nlin/0103011},
year = {2009}
}
Comments
10 pages, pLatex file