{"paper":{"title":"Reconstruction of chaotic systems in invariant jet space","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.SY","nlin.CD"],"primary_cat":"eess.SY","authors_text":"Evgeny Nikulchev","submitted_at":"2026-06-21T14:08:42Z","abstract_excerpt":"Takens' theorem is the gold standard for attractor reconstruction from time series, but it guarantees only topological equivalence and does not preserve metric or group properties such as symmetries. We show that switching from delay-coordinate space to jet space (signal and its derivatives) allows one to exactly preserve the symmetry group of the original system. This statement is rigorously justified by a theorem on the isomorphism of Lie algebras under jet prolongation. Numerical experiments on the Lorenz and R\\\"ossler systems confirm that jet-space reconstruction preserves geometry and sym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24929","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/2606.24929/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"}