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A positive answer to a symmetry conjecture on homogeneous IFS

Junda Zhang

Abstract

We positively answer `Open Question 1' in the paper of Feng and Wang [Adv. Math. 222 (2009)].

A positive answer to a symmetry conjecture on homogeneous IFS

Abstract

We positively answer `Open Question 1' in the paper of Feng and Wang [Adv. Math. 222 (2009)].
Paper Structure (3 theorems, 34 equations)

This paper contains 3 theorems, 34 equations.

Key Result

Theorem 1

Let $\Phi$ and $\Psi$ be two homogeneous IFSs satisfying the OSC, with the same attractor $K\subset\mathbb{R}$, and the common contraction factor being opposite to each other. Then $K$ is symmetric.

Theorems & Definitions (6)

  • Theorem 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • proof : Proof of the Theorem