{"paper":{"title":"Why Instantaneous Values of the \"Covariant\" Lyapunov Exponents Depend upon the Chosen State-Space Scale","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Carol G. Hoover, Wm. G. Hoover","submitted_at":"2013-09-09T23:20:15Z","abstract_excerpt":"We explore a simple example of a chaotic thermostated harmonic-oscillator system which exhibits qualitatively different local Lyapunov exponents for simple scale-model constant-volume transformations of its coordinate q and momentum p : { q,p } --> { (Q/s),(sP) } . The time-dependent thermostat variable zeta(t) is unchanged by such scaling. The original (q,p,zeta) motion and the scale-model (Q,P,zeta) version of the motion are physically identical. But both the local Gram-Schmidt Lyapunov exponents and the related local \"covariant\" exponents change with the change of scale. Thus this model fur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2342","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}