Back to Search
Start Over
A separation property for iterated function systems of similitudes
- Publication Year :
- 2022
-
Abstract
- Let $E$ be the attractor of an iterated function system $\{\phi_i(x)=\rho R_ix+a_i\}_{i=1}^N$ on $\Bbb R^d$, where $0<\rho<1$, $a_i\in \Bbb R^d$ and $R_i$ are orthogonal transformations on $\Bbb R^d$. Suppose that $\{\phi_i\}_{i=1}^N$ satisfies the open set condition, but not the strong separation condition. We show that $E$ can not be generated by any iterated function system of similitudes satisfying the strong separation condition. This gives a partial answer to a folklore question about the separation conditions on the generating iterated function systems of self-similar sets.
- Subjects :
- Mathematics - Dynamical Systems
Mathematics - Classical Analysis and ODEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2208.04042
- Document Type :
- Working Paper