分段扩张仿射映射的排斥子的维数
动力系统
2020-03-09 v3
摘要
本文研究 Michael Barnsley 所提出的一类欧氏空间中分段仿射系统的维数理论，并给出其在分形图像压缩中的一些应用。该类系统是 Keane、Simon 和 Solomyak 的论文 [The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition. Fund. Math., 180(3):279-292, 2003] 中所考虑类的更一般版本，并可视为作者们的工作 [On the dimension of self-affine sets and measures with overlaps. Proc. Amer. Math. Soc., 144(10):4427-4440, 2016]、[On the dimension of triangular self-affine sets. Erg. Th. & Dynam. Sys., to appear.] 的延续。我们还给出了所得结果在广义 Takagi 函数和分形插值函数中的一些应用。
引用
@article{arxiv.1803.03788,
title = {Dimension of the repeller for a piecewise expanding affine map},
author = {Balázs Bárány and Michał Rams and Károly Simon},
journal= {arXiv preprint arXiv:1803.03788},
year = {2020}
}