Algebraic entropy and the space of initial values for discrete dynamical systems
Algebraic entropy and the space of initial values for discrete dynamical systems
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离散动力系统的代数熵和初始值空间
DOI：
10.1088/0305-4470/34/48/317
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
T. Takenawa
中科院分区：
文献类型：
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作者：
T. Takenawa
给出了一种计算映射的代数熵的方法，该映射可以提升到一个合适的有理曲面（初值空间）的同构。证明了这类映射的第n阶的次数是由它在初值空间的Picard群上的作用给出的。通过构造还证明了Sakai列表中的每一个Painleve方程的第n阶的次数都是O（n ~ 2），因此它的代数熵为零。
A method to calculate the algebraic entropy of a mapping, which can be lifted to an isomorphism of a suitable rational surface (the space of initial values), is presented. It is shown that the degree of the nth iterate of such a mapping is given by its action on the Picard group of the space of initial values. It is also shown by construction that the degree of the nth iterate of every Painleve equation in Sakai's list is O(n2) and therefore its algebraic entropy is zero.