The Basilica Group is the iterated monodromy group associated with the Basilica map $z^2-1$. The Schur renormalization transformation describes the relation between the densities of states in various scales. For this group, it happens to be a rational map in two variables. We will describe the dynamical structure of this map that yields the laminar structure for the associated Green current (restricted to the real plane). It implies that the density of states for this group is a Cantor set of positive Lebesgue measure.
It is a joint work with E.Bedford, N.-B. Dang, and R.Grigorchuk.
By Jeremie Brieussel
By Ivan Mitrofanov
By Rostislav Grigorchuk
By Alejandra Garrido
By Dominik Francoeur
By Yair Hartman
By Mikhail Lyubich
By Vadim Kaimanovich
By Anitha Thillaisundaram
By Mikael de la Salle
By Josh Frisch
By Marialaura Noce
By Yves de Cornulier
By Clément Delcamp
By Ronnie Pavlov
By Tamara Kucherenko
