{"paper":{"title":"Lyapunov stability under $q$-dilatation and $q$-contraction of coordinates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Cesar Manchein, Eduardo Scafi, Marcus Werner Beims, Silvio Zanin, Tulio Meneghelli de Oliveira, Vinicius Wiggers","submitted_at":"2024-11-27T19:00:50Z","abstract_excerpt":"This study examines the Lyapunov stability under coordinate $q$-contraction and $q$-dilatation in three dynamical systems: the discrete-time dissipative H\\'enon map, and the conservative, non-integrable, continuous-time H\\'enon-Heiles and diamagnetic Kepler problems. The stability analysis uses the $q$-deformed Jacobian and $q$-derivative, with trajectory stability assessed for $q > 1$ (dilatation) and $q < 1$ (contraction). Analytical curves in the parameter space mark boundaries of distinct low-periodic motions in the H\\'enon map. Numerical simulations compute the maximal Lyapunov exponent a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18691","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/2411.18691/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"}