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Lectures of leading scientists at the Ural Mathematical Center (V. V. Sidorenko)

On December 12, an online seminar was held at the Ural Mathematical Center, at which V. V. Sidorenko, Doctor of Physical and Mathematical Sciences (Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, MIPT) gave a talk entitled “Integrable Models of the Secular Evolution of Motion in the Three-Body Problem.”

In his talk, the speaker linked the results of recent studies to the classical special cases of the three-body problem. In particular, the following issues were covered and discussed: the spatial doubly averaged restricted circular three-body problem (Sun–Jupiter–asteroid), the planar restricted three-body problem (inner and outer formulations), the Hill case and its role in the local approximation of motions close to the primary motion, the integrable case of the doubly averaged unrestricted three-body problem, the hierarchical three-body problem, and the application of the results to models of exoplanetary systems.
In concluding the seminar, the speaker emphasized that, despite significant progress in the construction of integrable models, one of the fundamental problems of modern celestial mechanics still remains open: the lack of a rigorous validation of the application of doubly averaged equations to the study of the secular evolution of motion.

The Ural Mathematical Center thanks V. V. Sidorenko and all seminar participants for the insightful discussion.