Jordi-Lluis Figueras
Department of Mathematics
Uppsala University
We will start by recalling a fundamental problem in mechanical systems: Stability of Solutions, and different approaches to attack it. One of them is the so-called KAM theory, originated in the 50s by Kolmogorov, Arnold and Moser. This theory gave certain hope in the characterization of stable motions, not only by proving the existence of quasi- periodic solutions but also revealing that they are present in regions of positive measure in phase space. However, the theory was for long time attributed to be seriously limited in the study of concrete and realistic problems.
We have shown that part of this scientific program is feasible in realistic mechanical systems, see [1]. I will finish the talk showing in general terms how we achieve it and an important ingredient that we consider would be of interest to the audience: rigorous Fast Fourier Transform.
Sources: [1] J.-Ll. Figueras, A. Haro, and A. Luque. Rigorous Computer-Assisted Application of KAM Theory: A Modern Approach. Found. Comput. Math., 17(5):1123-1193, 2017.