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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0811.2821","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-11-17T23:17:20Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"68503b3eedd3e435b048621568cf901aef4d391f8d64074e146cb06637911918","abstract_canon_sha256":"281b42ac97b0b428ffc27d4ba8b58085ffaad656619de639e77b6b5e5c9959ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:20.710608Z","signature_b64":"36fzUK5tdkWkYPZRj+/I7usgYMmXDqoDmrwLVTPpTjeUI664en/MHCtgFnWBKTNtcdeDnuQ5xiD4Zeo7Ar7ECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"795f6f8f3e915e8915cd7154fd251436e14805d796ace7679f874ba68e37d071","last_reissued_at":"2026-05-18T04:40:20.709989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:20.709989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\fR$. 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