{"paper":{"title":"Formal classification of unipotent parameterized diffeomorphisms","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Javier Rib\\'on","submitted_at":"2005-11-11T12:39:53Z","abstract_excerpt":"We provide a complete system of invariants for the formal classification of complex analytic unipotent germs of diffeomorphism at $\\cn{n}$ fixing the orbits of a regular vector field. We reduce the formal classification problem to solve a linear differential equation. Then we describe the formal invariants; their nature depends on the position of the fixed points set $Fix \\phi$ with respect to the regular vector field preserved by $\\phi$. We get invariants specifically attached to higher dimension ($n \\geq 3$) although generically they are analogous to the one-dimensional ones."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511298","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"}