Smooth conjugacy of difference equations derived from elliptic curves
Smooth conjugacy of difference equations derived from elliptic curves
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椭圆曲线导出的差分方程的平滑共轭
DOI：
10.1080/10236198.2021.1984441
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Sasha Glendinning
中科院分区：
文献类型：
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作者：
P. Glendinning;Sasha Glendinning
我们描述了与椭圆曲线的切线构造相关的动力学，它依赖于两个参数。除了参数平面上的半曲线外，这些映射的自然紧化被证明是光滑的（即）相互共轭并与经典混沌映射（切比雪夫多项式）共轭。这提供了一类彼此光滑共轭的映射的一个新的非平凡的例子。
We describe the dynamics associated with a construction of tangent lines to elliptic curves which depend on two parameters. With the exception of a half-curve in the parameter plane, the natural compactifications of these maps are shown to be smooth (i.e. ) conjugate to each other and to the classic chaotic map (Chebyshev polynomial) . This provides a new non-trivial example of a class of maps which are smooth conjugate to each other.