{"paper":{"title":"Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alfonso Blasco, Francisco J.Herranz, Ivan Gutierrez-Sagredo","submitted_at":"2022-06-25T19:04:13Z","abstract_excerpt":"We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by $$\\mathcal H_N = p_1^2 + p_2^2 +\\sum_{n=1}^N \\gamma_n(q_1 p_1 + q_2 p_2)^n ,$$ where $q_i$ and $p_i$ are generic canonical variables, $\\gamma_n$ are arbitrary coefficients, and $N\\in \\mathbb N$. For $N=2$, being both $\\gamma_1,\\gamma_2$ different from zero, this reduces to the classical Zernike system. We prove that $\\mathcal H_N$ always provides a superintegrable system (for any value of $\\gamma_n$ and $N$) by obtaining the corresponding constants of the motion explicitly, which turn out to be of hi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.12717","kind":"arxiv","version":2},"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/2206.12717/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"}