Abstract

The stability of the dynamics of the objects in the Solar system is a topic of paramount importance in Celestial Mechanics. Given the different time scales of natural and artificial objects, the mathematical methods to investigate the stability vary from perturbation theory, to Nekhoroshev’s theorem, to KAM theory. These theories are constructive in the sense that they give explicit estimates on the parameters of the system providing the stability. In particular, perturbation theory gives stability results on finite times, Nekhoroshev’s theorem gives effective stability on exponentially long times, KAM theory guarantees stability for infinite times in low-dimensional systems. We will also show that perturbative methods can be combined with Machine Learning techniques, in particular to analyze the dynamics of groups of objects, for example to classify and cluster space debris generated by break-up events of artificial satellites.

Short Bio

Alessandra Celletti is a renowned mathematician with expertise in dynamical systems and celestial mechanics. She earned her Ph.D. from ETH Zurich and is currently a full professor at the University of Rome Tor Vergata.

Celletti has authored over a hundred publications and has held numerous leadership roles in academic and scientific institutions, both in Italy and abroad. Internationally recognized for her contributions to mathematics and science outreach, she is also deeply engaged in research evaluation, currently serving as a Member of the Governing Board and Vice-President of ANVUR, the Italian National Agency for the Evaluation of Universities and Research Institutes. Over the years, she has coordinated and participated in various high-impact national and European research projects, including the European “Marie Curie Initial Training Network” projects Astronet, Stardust, and Stardust-R, as well as projects funded by the Italian Space Agency and PRIN-MIUR. In her honor, asteroid 2005 DJ1, n. 117539, has been named “Alessandra Celletti”.

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