Mould calculus and normalization of vector fields or diffeomorphisms I

SEMINARI DI SISTEMI DINAMICI OLOMORFI (e dintorni)

ABSTRACT

This talks will provide an introduction to mould calculus, as introduced by Jean Ecalle. We shall give a precise definition of moulds and describe their main properties, and we shall apply this formalism to the problem of normal forms for vector fields and iffeomorphisms.

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Mould calculus and normalization of vector fields or diffeomorphisms

SEMINARI DI SISTEMI DINAMICI OLOMORFI (e dintorni)

ABSTRACT

This talks will provide an introduction to mould calculus, as introduced by Jean Ecalle. We shall give a precise definition of moulds and describe their main properties, and we shall apply this formalism to the problem of normal forms for vector fields and diffeomorphisms.

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A Transmission Strategy for Hyperbolic Internal Waves of Small Width

Argomento: Analisi 

Abstract: 

Semilinear hyperbolic problems with
source terms piecewise smooth and discontinuous across characteristic surfaces yield similarly piecewise smooth solutions.  If the discontinuous source is replaced with a smooth transition layer, the discontinuity of the solution is replaced by a smooth internal layer. In this paper we describe how the layer structure of the solution can be computed from the layer structure of the source in the limit of thin layers. The key idea is to use a transmission problem strategy for the problem with the smooth internal layer.  That leads to an ansatz different from the obvious candidates. The obvious candidates lead to overdetermined equations for correctors.  With the transmission problem strategy we compute infinitely accurate expansions.

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