• C. SABOT

Code(s) de Classification MSC:

• 37F10 Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]
• 32H50 Iteration problems
• 53D10 Contact manifolds, general
• 94C99 None of the above, but in this section
• 28A80 Fractals [See also 37Fxx]

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