Instabilities in Hamiltonian systems:
a study of the original Arnold model

https://www.crm.cat/seminar-sijimat/



Date: Thursday 8th, June 2023.
Time: 12h
Place: Aula petita CRM.

Abstract:

The goal of this talk is to introduce the concept of Arnold diffusion, to explain where it lies inside the area of study of differential equations and to present my specific research topic. First we will contextualize the study of Arnold diffusion. For that, we will trace historically the development of the area of Hamiltonian systems highlighting the question of stability and its importance for physical models. Then, we will look at the more abstract mathematical setting of perturbation theory developed to tackle the problem of stability. We will define Arnold diffusion and we will outline the relevant questions researchers are interested in. Finally, I will focus on my study of Arnold’s original problem using modern techniques of analysis of exponentially small phenomena.

SPEAKER
Román Moreno
Román Moreno

Universitat Politècnica de Catalunya

PhD student in the Dynamical Systems group at UPC, working with Immaculada Balrdomá and Tere M. Seara on the role of resonances in Arnold Diffusion.
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