English

A positive answer to a symmetry conjecture on homogeneous IFS

Dynamical Systems 2026-03-17 v2

Abstract

If two homogeneous IFSs satisfying the OSC with opposite common contraction factors share the same attractor on the real line, we show that this attractor is symmetric. This answers a question of Feng and Wang [Adv. Math. 222 (2009), 1964-1981].

Keywords

Cite

@article{arxiv.2603.11062,
  title  = {A positive answer to a symmetry conjecture on homogeneous IFS},
  author = {Junda Zhang},
  journal= {arXiv preprint arXiv:2603.11062},
  year   = {2026}
}