{"paper":{"title":"Chebyshev polynomials on generalized Julia sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"G\\\"okalp Alpan","submitted_at":"2015-04-30T15:45:30Z","abstract_excerpt":"Let $(f_n)_{n=1}^\\infty$ be a sequence of nonlinear polynomials satisfying some mild conditions. Furthermore, let $F_m(z)=(f_m\\circ f_{m-1}\\ldots \\circ f_1)(z)$ and $\\rho_m$ be the leading coefficient for $F_m$. It is shown that on the Julia set $J_{(f_n)}$, the Chebyshev polynomial of the degree deg${F_m}$ is of the form $F_m(z)/\\rho_m-\\tau_m$ for all $m\\in\\mathbb{N}$ where $\\tau_m\\in\\mathbb{C}$. This generalizes the result obtained for autonomous Julia sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08278","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"}