一类单无界变差点的连续函数的分形维数估计
Estimation of Fractal Dimension of a Classof Continuous Functionwith SingleUnbounded Variable Difference
DOI: 10.12677/PM.2023.135137, PDF, HTML, 下载: 244  浏览: 291  国家自然科学基金支持
作者: 任倩倩*, 梁永顺：南京理工大学, 数学与统计学院, 江苏 南京
关键词: 分形维数；无界变差点；Weierstrass 函数；Fractal Dimension； Unbounded Variation； Weierstrass Function
摘要: 在本文中，我们主要在闭区间上构造了仅有一个无界变差点的连续函数。接着讨论了它的分形维数，该函数图像的分形维数严格大于其拓扑维数。尽管该连续函数只在零点处不可微，但仍具有明显的分形特征。
Abstract: In this paper, we mainly construct a continuous function with only one unbounded variable difference on closed intervals. Then we discuss its fractal dimension. The fractal dimension of the function image is strictly larger than its topological dimension. Although the given function is only nondifferentiable at the zero point, it still has obvious fractal characteristics.
文章引用：任倩倩, 梁永顺. 一类单无界变差点的连续函数的分形维数估计[J]. 理论数学, 2023, 13(5): 1341-1354. https://doi.org/10.12677/PM.2023.135137

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