IFS attractors and Cantor sets

Sylvain Crovisier (1) , Michal Rams (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 Instytut Matematyczny PAN

We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R^3 such that every homeomorphism f of R^3 which preserves K coincides with the identity on K.

Domaines: Systèmes dynamiques [math.DS]

Sylvain Crovisier, Michal Rams. IFS attractors and Cantor sets. Topology and its Applications, 2006, 153 (11), pp.1849-1859. ⟨10.1016/j.topol.2005.06.010⟩. ⟨hal-00538127⟩