Séminaire Géométrie Topologie Dynamique
Spectral Renormalization of the Basilica Group
09
déc. 2021
déc. 2021
| Intervenant : | Mikhail Lyubich |
| Institution : | Stony Brook |
| Heure : | 14h00 - 15h00 |
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 Laplacian spectra 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. It implies that the spectrum of this group is a
Cantor set of positive Lebesgue measure.
Basilica map z^2-1. The Schur renormalization transformation describes the
relation between the Laplacian spectra 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. It implies that the spectrum of this group is a
Cantor set of positive Lebesgue measure.
It is a joint with E.Bedford, N.-B. Dang, and R.Grigirchuk.
N.B. Le séminaire sera diffusé en direct sur https://webconf.imo.universite-paris-saclay.fr/b/jer-7cp-7mk (sauf problèmes techniques)