Talk 6

Title: Frozen-Planet Orbits in Helium Model

Speaker:  Lei Zhao

Affiliation:  Dalian University of Technology (DUT)

Abstract: A frozen-planet orbit in the classical Helium model is a particular collinear generalized periodic orbit along which both electrons appear on the same side of the nucleus, the inner electron falls into the nucleus and bounces back, while the outer one librates. It was numerically known since quite some time and played an important role in the semi-classical investigation of the quantum Helium model. A first proof of its existence as well as some counting information appeared in 2023 in two papers by Cieliebak-Frauenfelder-Volkov. I presented a simple proof in the same year. This line of investigation was further carried out in Turin: Baranzini-Canneori-Terracini have made two generalizations in 2024 and 2025. In this talk I shall review these works and also indicate some open problems.