论文标题
双曲数的二次动态
Quadratic Dynamics Over Hyperbolic Numbers
论文作者
论文摘要
双曲数是复数的变化，但它们的动态却大不相同。双曲线数字上的二次函数的双曲线曼德布罗特设置只是一个填充的正方形，而双曲线曼德布罗特（双曲线曼德布罗特）内的双曲线参数的填充仪集是一个填充的矩形。对于双曲线式Mandelbrot集外的双曲线参数，填充的Julia Set具有3个可能的拓扑描述，如果不是空的，则与始终是一个完全完全断开连接的复杂情况相反。这些结果在[1,2,4,5,6,7]中得到了证明，并在此处进行了审查
Hyperbolic numbers are a variation of complex numbers, but their dynamics is quite different. The hyperbolic Mandelbrot set for quadratic functions over hyperbolic numbers is simply a filled square, and the filled Julia set for hyperbolic parameters inside the hyperbolic Mandelbrot set is a filled rectangle. For hyperbolic parameters outside the hyperbolic Mandelbrot set, the filled Julia set has 3 possible topological descriptions, if it is not empty, in contrast to the complex case where it is always a non-empty totally disconnected set. These results were proved in [1,2,4,5,6,7] and are reviewed here
