{"paper":{"title":"Relative Periodic Orbits in the Gutzwiller-type Anisotropic Kepler Problem and $n$-body Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.SG"],"primary_cat":"math.DS","authors_text":"Xijun Hu, Yifan Yang, Yuwei Ou, Zhiwen Qiao","submitted_at":"2026-08-13T07:35:47Z","abstract_excerpt":"We study the relative periodic orbits in the Gutzwiller-type anisotropic Kepler problem, which is a generalized model derived from the classical Gutzwiller anisotropic Kepler problem. By reducing the rotational symmetry of the $z$-axis, we obtain a reduced system with two degrees of freedom and its energy surface forms a compact and regular three-sphere in a certain parameter range. Combining the estimation of the Seifert rotation number of the planar Kepler orbit and the CHHL formula introduced in \\cite{CHHL23}, we prove that this system admits infinitely many periodic orbits on every compact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12901","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.12901/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}