The space of initial conditions and the property of an almost good reduction in discrete Painlevé II equations over finite fields
- 10.1080/14029251.2013.862437How to use a DOI?
- discrete Painlevé equation; finite field; good reduction; space of initial condition
We investigate the discrete Painlevé equations (dPII and 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.
- © 2013 The Authors. Published by Atlantis Press and Taylor & Francis
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Cite this article
TY - JOUR AU - Masataka Kanki AU - Jun Mada AU - Tetsuji Tokihiro PY - 2021 DA - 2021/01/06 TI - The space of initial conditions and the property of an almost good reduction in discrete Painlevé II equations over finite fields JO - Journal of Nonlinear Mathematical Physics SP - 101 EP - 109 VL - 20 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.862437 DO - 10.1080/14029251.2013.862437 ID - Kanki2021 ER -