The space of initial conditions and the property of an almost good reduction in discrete Painleve II equations over finite fields
The space of initial conditions and the property of an almost good reduction in discrete Painleve II equations over finite fields
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有限域上离散Painleve II方程的初始条件空间和几乎良好约简的性质
DOI：
10.1080/14029251.2013.862437
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发表时间：
2013
影响因子：
0.7
通讯作者：
Masataka
中科院分区：
文献类型：
--
作者：
KANKI;Masataka
研究了有限域上离散的Painlevé方程（dPII和qPII）.我们首先表明，它们是很好地定义根据理论的初始条件的空间通过扩展域。然后，我们对待他们在当地的领域，并观察到他们有一个属性，这是类似于良好的减少动力系统在有限域。我们可以利用这个性质，它可以被解释为一个算术模拟的奇异禁闭，以避免不确定性的方程在有限域和获得特殊的解决方案，从原来定义的领域的特征零。
We investigate the discrete Painlevé equations (dPIIand qPII) over finite fields. We first show that they are well defined by extending the domain according to the theory of the space of initial conditions. Then we treat them over local fields and observe that they have a property that is similar to the good reduction of dynamical systems over finite fields. We can use this property, which can be interpreted as an arithmetic analogue of singularity confinement, to avoid the indeterminacy of the equations over finite fields and to obtain special solutions from those defined originally over fields of characteristic zero.