Paper

On the group of isometries of planar IFS fractals*

and

Published 3 December 2021 • © 2021 IOP Publishing Ltd & London Mathematical Society
, , Citation Qi-Rong Deng and Yong-Hua Yao 2022 Nonlinearity 35 445 DOI 10.1088/1361-6544/ac3924

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dengfractal@126.com

1157208805@qq.com

Author affiliations

1 College of Mathematics and Statistics, Center for Applied Mathematics of Fujian Province & Fujian Key Laboratory of Mathematical Analysis and Applications (FJKLMAA), Fujian Normal University, Fuzhou, Fujian province, 350117, China

Author notes

2 Authors to whom any correspondence should be addressed.

3 Recommended by Dr Lorenzo J Diaz.

Dates

  1. Received 17 March 2021
  2. Revised 8 November 2021
  3. Accepted 12 November 2021
  4. Published

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0951-7715/35/1/445

Abstract

For any iterated function system (IFS) on ${\mathbb{R}}^{2}$, let K be the attractor. Consider the group of all isometries on K. If K is a self-similar or self-affine set, it is proven that the group must be finite. If K is a bi-Lipschitz IFS fractal, the necessary and sufficient conditions for the infiniteness (or finiteness) of the group are given. For the finite case, the computation of the size of the group is also discussed.

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Footnotes

  • * 

    The work is supported by NSFC (No. 11971109). The first author is partially supported by the Program for Probability and Statistics: Theory and Application (No. IRTL1704), and the program for innovative research team in science and technology in Fujian province university (No. IRTSTFJ).

10.1088/1361-6544/ac3924