Abstract
AbstractA symmetry of a Hamiltonian system is a symplectic or anti-symplectic involution which leaves the Hamiltonian invariant. For the planar and spatial Hill lunar problem, four resp. eight linear symmetries are well-known. Algebraically, the planar ones form a Klein four-group$${\mathbb {Z}}_2 \times {\mathbb {Z}}_2$$Z2×Z2and the spatial ones form the group$${\mathbb {Z}}_2 \times {\mathbb {Z}}_2 \times {\mathbb {Z}}_2$$Z2×Z2×Z2. We prove that there are no other linear symmetries. Remarkably, in Hill’s system the spatial linear symmetries determine already the planar linear symmetries.
Funder
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
Publisher
Springer Science and Business Media LLC
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