{"paper":{"title":"On Analytic Perturbations of a Family of Feigenbaum-like Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Denis Gaidashev","submitted_at":"2008-11-17T23:17:20Z","abstract_excerpt":"We prove existence of solutions $(\\phi,\\lambda)$ of a family of of Feigenbaum-like equations \\label{family} \\phi(x)={1+\\eps \\over \\lambda} \\phi(\\phi(\\lambda x)) -\\eps x +\\tau(x), where $\\eps$ is a small real number and $\\tau$ is analytic and small on some complex neighborhood of $(-1,1)$ and real-valued on $\\fR$. The family $(\\ref{family})$ appears in the context of period-doubling renormalization for area-preserving maps (cf. \\cite{GK}).\n  Our proof is a development of ideas of H. Epstein (cf \\cite{Eps1}, \\cite{Eps2}, \\cite{Eps3}) adopted to deal with some significant complications that arise"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.2821","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"}