Integrable mappings of the plane preserving biquadratic invariant curves II
Integrable mappings of the plane preserving biquadratic invariant curves II
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保留双二次不变曲线的平面的可积映射 II
DOI：
10.1088/0951-7715/15/2/313
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发表时间：
2002
期刊：
影响因子：
1.7
通讯作者：
J. Roberts
中科院分区：
文献类型：
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作者：
Apostolos Iatrou;J. Roberts
我们回顾了最近引入的曲线相关麦克米伦映射，它是平面的映射，保持双二次叶状。我们证明了它们是保测度的，因此是可积的。我们讨论了这些映射的几何性质，包括它们的不动点和稳定性。考虑对称和非对称双二次曲线的正规形式及其相关的麦克米伦映射的正规形式。考虑了用雅可比椭圆函数或有理函数参数化双二次曲线的可能性，进一步讨论了双二次曲线上的动力学问题。
We review recently introduced curve-dependent McMillan maps which are mappings of the plane that preserve biquadratic foliations. We show that they are measure preserving and thus integrable. We discuss the geometry of these maps including their fixed points and their stability. We consider the normal forms of symmetric and asymmetric biquadratic curves and the normal forms for their associated McMillan maps. We further discuss the dynamics on biquadratic curves by considering the possibility of parametrizing them by Jacobian elliptic or rational functions.
离散Painleve方程的自治极限
DOI：
--
发表时间：
2002
期刊：
Physica A Vol. 305
影响因子：
--
作者：
K.Asano;F.Takahara;A.Ramani
通讯作者：
A.Ramani