Algebraic entropy of an extended Hietarinta-Viallet equation
Algebraic entropy of an extended Hietarinta-Viallet equation
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扩展 Hietarinta-Viallet 方程的代数熵
DOI：
10.1088/1751-8113/48/35/355202
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Takafumi Mase and Tetsuji Tokihiro
中科院分区：
文献类型：
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作者：
Masataka Kanki;Takafumi Mase and Tetsuji Tokihiro
我们引入了一系列离散映射，它被认为是单参数Hietarinta-Viallet映射的推广。通过得到迭代映象次数的递推关系，得到了该映象的代数熵。对于某些参数值，该映射具有限定奇异性，在这种情况下，该映射等价于六个不可约多项式之间的递推关系。对于其他参数值，映射不通过奇点约束测试。术语的不可约性和协素性在讨论中起着至关重要的作用。
We introduce a series of discrete mappings, which is considered to be an extension of the Hietarinta–Viallet mapping with one parameter. We obtain the algebraic entropy for this mapping by obtaining the recurrence relation for the degrees of the iterated mapping. For some parameter values the mapping has a confined singularity, in which case the mapping is equivalent to a recurrence relation between six irreducible polynomials. For other parameter values, the mapping does not pass the singularity confinement test. The properties of irreducibility and co-primeness of the terms play crucial roles in the discussion.