{"paper":{"title":"Extensive Properties of the Complex Ginzburg-Landau Equation","license":"","headline":"","cross_cats":["nlin.CD","nlin.PS","patt-sol"],"primary_cat":"chao-dyn","authors_text":"Jean-Pierre Eckmann, Pierre Collet","submitted_at":"1998-02-06T07:25:42Z","abstract_excerpt":"We study the set of solutions of the complex Ginzburg-Landau equation in $\\real^d, d<3$. We consider the global attracting set (i.e., the forward map of the set of bounded initial data), and restrict it to a cube $Q_L$ of side $L$. We cover this set by a (minimal) number $N_{Q_L}(\\epsilon)$ of balls of radius $\\epsilon$ in $\\Linfty(Q_L)$. We show that the Kolmogorov $\\epsilon$-entropy per unit length, $H_\\epsilon =\\lim_{L\\to\\infty} L^{-d} \\log N_{Q_L}(\\epsilon)$ exists. In particular, we bound $H_\\epsilon$ by $\\OO(\\log(1/\\epsilon)$, which shows that the attracting set is smaller than the set o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9802006","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":""},"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"}