mercoledi' - 14-04-2004 (11:00 - Aula Riunioni* del Centro di Ricerca Matematica Ennio De Giorgi palazzo Puteano) : Etienne Ghys

Fatou and Julia sets for holomorphic foliations argomento: "Geometria" e "Analisi Matematica".

abstract: SEMINARIO DI SISTEMI DINAMICI (olomorfi e dintorni) D. Sullivan noticed a strong analogy between the dynamics of rational maps, kleinian groups, and (transversaly) holomorphic foliations. In this talk, I would like to discuss a joint work with Gomez-Mont and Saludes in which we try to generalize (as much as possible) the Julia-Fatou theory and the "non wandering theorem" in the context of foliations.

giovedi' - 15-04-2004 (17:00 - Sala Seminari) : Vladimir Gerdt

Algorithmic Generation of Finite Difference Schemes for Differential Equations

abstract: We present an algorithmic technique for construction of fully conservative finite difference schemes for partial differential equations. This technique based on discretization of the initial equation in its conservation law form together with some extra integral relations. It yields an algebraic system for discrete values of the sought functions and its derivatives. The difference scheme is obtained by elimination of the derivatives what can be done by construction of an appropriate pure algebraic Groebner or involutive basis. We demonstrate the technique by the classical Laplace equation, heat equation and wave equation. As a nontrivial example we consider also nonlinear Falkowich-Karman equation describing transonic flow in gas dynamics.

Giulia Curciarello Segreteria Didattica tel: 050-2213219 e-mail curciare@dm.unipi.it

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