Cai-Yun Ma (HUN-REN–BME Stochastics Research Group, BME): Separation Conditions for Iterated Function Systems with a Common Attractor

Let \(K \subset \mathbb{R}^d\) be a non-singleton self-similar set generated by a finite iterated function system (IFS) of contracting similitudes satisfying the open set condition (OSC) but not the strong separation condition (SSC). Can we find another finite IFS of similitudes satisfying the SSC that also generates \(K\)? In this talk, we show that the answer is no. This result removes the homogeneity assumption from a result of Feng, Ruan and Xiong and gives a negative answer to a folklore question about separation conditions for generating iterated function systems of self-similar sets.

Zoom:  https://us02web.zoom.us/j/83725792437?pwd=9Zhxb4WEwTnPIEwo5raP2pMRan7q5n.1
Meeting ID: 837 2579 2437
Passcode: 003478