Random affine code tree fractals and Falconer-Sloan condition

Orateur: LI Bing
Localisation: Université de technologie de Chine méridionale, Chine
Type: Séminaire COOL
Site: Hors LAMA , IHP
Salle: 5
Date de début: 18/09/2015 - 11:10
Date de fin: 18/09/2015 - 11:10

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.