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GDMSeminar: Abstracts of the Talks (2022/2)

Daniel Strzelecki (Nicolaus Copernicus University, ToruĊ„, Poland)

Lyapunov center theorem  for Hamiltonian systems with symmetries

Tuesday, February 15, 2022, 16:00 GMT

Abstract: Classical Lyapunov center theorem is an useful result but can not be applied when critical points are not isolated. In the presence of symmetries of a compact Lie group  critical points form orbits of the group action. I am going to present the symmetric version of the Lyapunov center theorem where the crucial assumptions are given in the terms of Brouwer degree and Morse index. Some applications to problems from celestial mechanics will be shown.