## Random affine code tree fractals and Falconer-Sloan condition

Type:
Type:
Site:
Date:
18/09/2015 - 11:10 - 12:10
Salle:
05
Orateur:
LI Bing
Localisation:
Université de technologie de Chine méridionale
Localisation:
République populaire de Chine
Résumé:

We calculate the almost sure dimension for a general class of random affine code tree fractals in $\mathbb R^d$. The result is based on a probabilistic version of the Falconer-Sloan condition $C(s)$ introduced in Falconer and Sloan (2009). We verify that, in general, systems having a small number of maps do not satisfy condition $C(s)$. However, there exists a natural number $n$ such that for typical systems the family of all iterates up to level $n$ satisfies condition $C(s)$. This is a joint work with Esa Järvenpää, Maarit Järvenpää, and Örjan Stenflo.