Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Symplectic geometrical aspects of the renormalization map of self-similar lattices

Auteur(s):

Code(s) de Classification MSC:

Résumé: We present the renormalization map we introduced in [23] in order to describe the spectral properties of self-similar lattices, from the point of view of symplectic geometry. We show that this map comes from a symplectic reduction and that its key-properties come from general properties of symplectic reductions, that we prove in this text. In particular, the singularities of the symplectic reduction, considered as a rational map, are explicitly described and play an important role. We also present new examples, where we can compute the renormalization map.

Mots Clés: Spectral theory ; Symplectic geometry ; Symplectic reductions ; Lagrangian Grassmannians ; Fractal geometry ; Laplace operators on fractals ; Dirichlet forms

Date: 2003-03-12

Prépublication numéro: PMA-806

Front pages.

Postscript file : PMA-806.ps