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arXiv · 2607.03244

Relative Periodic Orbits in the Spatial Anisotropic Kepler Problem

Xijun Hu·Yuwei Ou·Zhiwen Qiao
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Abstract

The spatial anisotropic Kepler problem comes from quantum mechanics, which models electron motion in semiconductors with donor impurities and depends on the anisotropic parameter $\beta\in(-1,+\infty)$. After reducing the system modulo rotational symmetry, we investigate periodic orbits in this two-degree-of-freedom setting. Combining an index comparison in \cite{HLOQS26}, the volume formula in \cite{CHHL23} and Franks' theorem, we prove that the system possesses infinitely many periodic orbits on any fixed compact and regular energy surface for $\beta\in(-1,0]$.

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Xijun Hu, Yuwei Ou, Zhiwen Qiao. 2026-07-03. Relative Periodic Orbits in the Spatial Anisotropic Kepler Problem. https://doi.org/10.3934/dcds.2026057

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