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Algebraic entropy and the space of initial values for discrete dynamical systems

Tomoyuki Takenawa
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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 $n$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 $n$th iterate of every Painlevé equation in sakai's list is at most $O(n^2)$ and therefore its algebraic entropy is zero.

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Tomoyuki Takenawa. 2001-05-01. Algebraic entropy and the space of initial values for discrete dynamical systems. https://doi.org/10.1088/0305-4470%2F34%2F48%2F317

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