论文标题
仿射分形的持久景观
The Persistence Landscapes of Affine Fractals
论文作者
论文摘要
我们开发了一种使用相应转换的参数来计算仿生分形的持久景观的方法。鉴于迭代的仿射转换功能系统满足了一定的兼容条件，我们证明存在着仿射转换作用在持久景观空间上的仿射变换，该景观景观空间交织了迭代功能系统的作用。后一种仿射转化是严格的收缩，其独特的固定点是仿射分形的持久性景观。我们介绍了该理论的几个例子，并通过模拟确认了主要结果。
We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility condition, we prove that there exists an affine transformation acting on the space of persistence landscapes which intertwines the action of the iterated function system. This latter affine transformation is a strict contraction and its unique fixed point is the persistence landscape of the affine fractal. We present several examples of the theory as well as confirm the main results through simulations.
