{"paper":{"title":"Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.AP","authors_text":"Athanasios Chatzikaleas, Jacques Smulevici","submitted_at":"2025-02-07T11:00:49Z","abstract_excerpt":"Given any wave operator with principle part $\\partial_{t}^2 -\\partial_{x}^2 +\\mathcal{B}^{xx}(\\omega t,x)\\partial_{x}^2$, where $\\mathcal{B}^{xx}:\\mathbb{T}^{\\nu+1} \\rightarrow \\mathbb{R}$ is a sufficiently small, quasi-periodic perturbation and $\\omega \\in \\mathbb{R}^\\nu$, we explain how to construct \\emph{null coordinates} that respect the quasi-periodicity of the solutions. As it turns out, in these coordinates, the principal symbol of the wave operator above has constant coefficients. To construct these coordinates, we start by writing the wave operator in geometric form, modulo terms of o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.04826","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/2502.04826/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"}