Séminaire Analyse
organisé par l'équipe Analyse
-
Maja Resman
Analytic invariants of parabolic germs from their orbits
4 avril 2024 - 11:00Salle de conférences IRMA
This is joint work with Martin Klimes, Pavao Mardesic (University of Burgundy, France) and Goran Radunovic (University of Zagreb, Croatia), based on [KMRR]. The moduli of analytic classification of parabolic germs of diffeomorphisms, germified at a parabolic fixed point, are given by a finite number of diffeomorphisms, called the Horn- maps (Écalle, Voronin). We read the analytic invariants by fractal analysis of one orbit (i.e. one realization) of a diffeomorphism. The object that we study is the so-called theta function of one orbit, which, in the case of real orbits considered as fractal strings (introduced by Lapidus), is closely related to their fractal theta function. The fractal theta function of a fractal string is inspired by and generalizes the geometric zeta function of a fractal string (Lapidus). Standardly, fractal zeta functions talk about the geometry of a fractal string, its first singularity being the box dimension of the string. We show how to read the analytic class analysing the singularities of the theta function of one orbit in the integral plane. [KMRR] Klimes, M., Mardesic, P., Radunovic, G., Resman, M., Analytic invariants of a parabolic diffeomorphism from its orbit , accepted for publication in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (2023), https://arxiv.org/pdf/2112.14324.pdf -
Jean-Claude Saut
Autour des systèmes de Boussinesq
11 avril 2024 - 11:00Salle de conférences IRMA
On fera le point sur l'histoire, les résultats connus et les questions ouvertes, autour de systèmes pour la première fois obtenus par Joseph Boussinesq modélisant la propagation d'ondes faiblement non linéaire -
Gaetan Leclerc
TBA
16 mai 2024 - 11:00Salle de conférences IRMA
-
Yohann Genzmer
TBA
30 mai 2024 - 11:00Salle de conférences IRMA
-
Michele Ancona
TBA
27 juin 2024 - 11:00Salle de conférences IRMA