Arithmetic conditions on self-similar subsets

Type:
Type:
Site:
Date:
18/09/2015 - 10:00 - 11:00
Salle:
05
Orateur:
XIONG Ying
Localisation:
Université de technologie de Chine méridionale
Localisation:
République populaire de Chine
Résumé:

Let $E,F\subset\mathbb R^d$ be two self-similar sets. Let $\{\rho_i\}$ and $\{\gamma_j\}$ be the contraction ratios of $E$ and $F$, respectively. Suppose that $E$ satisfies the SSC and $F\subset E$. Under certain circumstances, we prove that there exist non-negative rational numbers $t_{i,j}$ such that $\gamma_j=\prod_i\rho_i^{t_{i,j}}$.