TY  - JOUR
A1  - Zhao, Lei
T1  - Shooting for collinear periodic orbits in the Helium model
T2  - Zeitschrift für angewandte Mathematik und Physik
N2  - The frozen-planet periodic orbit of the classical collinear Helium model with negative energy is shown to exist by a simple shooting argument. This simplifies the approach established in Cieliebak et al. (Ann Inst H Poincaré Anal Non Linéaire 40:379–455, 2022). With this argument, it also follows that the algebraic count of the number of such orbits with a given negative energy is 1, as recently established in Cieliebak et al. (Nondegeneracy and integral count of frozen-planet orbits in helium, 2022. arXiv:2209.12634). The same argument also leads to the existence of other collinear periodic orbits of the classical collinear Helium model.
KW  - Applied Mathematics
KW  - General Physics and Astronomy
KW  - General Mathematics
Y1  - 2023
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/109661
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-1096611
SN  - 0044-2275
SN  - 1420-9039
VL  - 74
IS  - 6
SP  - 227
PB  - Springer Science and Business Media LLC
ER  -