Blanc SIMI 1 - Sciences de l'information, de la matière et de l'ingénierie : Mathématiques et interactions

Dynamics and PDEs – DynPDE

Submission summary

The general framework of this project is the study of dynamical systems and partial differential equations. We are primarily
interested in those equations which appear either as infinite dimensional dynamical systems or as geometric structures. Our goal is
to study remarkable solutions, invariants manifolds as well as the corresponding local dynamical behavior. We are also interested in the
persistence of those solutions and invariant manifolds when the dynamical system is perturbed. One of the means that we propose to use
is that of normal forms. The latter are « simple » elements of the orbit of a dynamical system under the action of a subgroup of
diffeomorphisms of the phase space. They are a classical and powerful tool for finite dimensional dynamical systems which are not too
degenerate. Recently, this tool has been used successfully in the study of some evolution equations as well as some geometric
structures, such as Cauchy-Riemann structures, singular or not, or Poisson structures. The use of normal forms shows two main
difficulties: resonances, which are nothing but the obstructions to solve the linearized problem, and small divisors. The main goal of
this project is to develop these technics and to apply them to problems that come from geometrical problems, partial differential
equations and more classical dynamical systems. Although these problems are very different, they are conceptually very close and
their solutions will greatly benefit from the collaboration of mathematicians having different backgrounds and expertise.

Project coordination

Laurent STOLOVITCH (UNIVERSITE DE NICE - SOPHIA ANTIPOLIS) – stolo@unice.fr

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

Collège de France COLLEGE DE FRANCE
Nantes UNIVERSITE DE NANTES
UNIVERSITE DE NICE - SOPHIA ANTIPOLIS

Help of the ANR 220,000 euros
Beginning and duration of the scientific project: - 48 Months

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