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We present variational characterizations of frozen planet orbits for the helium atom in the Lagrangian and the Hamiltonian picture. They are based on a nonlocal Levi-Civita regularization in Barutello, Ortega and Verzini (2021) with different time reparametrizations for the two electrons and lead to nonlocal functionals. Within this variational setup, we deform the helium problem to one where the two electrons interact only by their mean values and use this to deduce the existence of frozen planet orbits.
@article{AIHPC_2023__40_2_379_0,
author = {Cieliebak, Kai and Frauenfelder, Urs and Volkov, Evgeny},
title = {A variational approach to frozen planet orbits in helium},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {379--455},
volume = {40},
number = {2},
year = {2023},
doi = {10.4171/aihpc/46},
language = {EN},
url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/46/}
}
TY - JOUR AU - Cieliebak, Kai AU - Frauenfelder, Urs AU - Volkov, Evgeny TI - A variational approach to frozen planet orbits in helium JO - Annales de l'I.H.P. Analyse non linéaire PY - 2023 SP - 379 EP - 455 VL - 40 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4171/aihpc/46/ DO - 10.4171/aihpc/46 LA - EN ID - AIHPC_2023__40_2_379_0 ER -
%0 Journal Article %A Cieliebak, Kai %A Frauenfelder, Urs %A Volkov, Evgeny %T A variational approach to frozen planet orbits in helium %J Annales de l'I.H.P. Analyse non linéaire %D 2023 %P 379-455 %V 40 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4171/aihpc/46/ %R 10.4171/aihpc/46 %G EN %F AIHPC_2023__40_2_379_0
Cieliebak, Kai; Frauenfelder, Urs; Volkov, Evgeny. A variational approach to frozen planet orbits in helium. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 2, pp. 379-455. doi: 10.4171/aihpc/46
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