3 décembre 2018

Juho Leppänen (Univ. Helsinki & IMJ)
Quasistatic dynamical systems with intermittency

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Lieu : salle 3L8

Résumé : Quasistatic dynamical systems (QDS), introduced by Dobbs and Stenlund around 2015, model dynamics that transform slowly over time due to external influences. They are generalizations of conventional dynamical systems and belong to the realm of deterministic non-equilibrium processes.
I will first define QDSs and then discuss an ergodic theorem, which is needed since the usual theorem due to Birkhoff does not apply in the absence of invariant measures. After briefly explaining some applications of the ergodic theorem, I will give results on the statistical properties of a particular QDS in which the evolution of states is described by intermittent Pomeau-Manneville type maps. One of these results is a functional central limit theorem, obtained by solving a well-posed martingale problem, which describes statistical behavior as a stochastic diffusion process.

Quasistatic dynamical systems with intermittency  Version PDF

Octavian Mitrea (University of Western Ontario, Canada)
A characterization of rationally convex immersions

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Lieu : IMO ; salle 3L8.

Résumé : Let S be a smooth, totally real, compact immersion in C^n of real dimension m \leq n, which is locally polynomially convex and it has finitely many points where it self-intersects finitely many times, transversely or non-transversely. Our result proves that S is rationally convex if and only if it is isotropic with respect to a « degenerate » Kähler form in C^n. We also show that there exists a large class of such rationally convex immersions that are not isotropic with respect to any genuine (non-degenerate) Kähler form.

A characterization of rationally convex immersions  Version PDF