{"paper":{"title":"Computational Complex Dynamics of $\\displaystyle{f_{\\alpha, \\beta, \\gamma, \\delta}(z)=\\frac{\\alpha z + \\beta}{\\gamma z^2 +\\delta z}}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sk. Sarif Hassan","submitted_at":"2016-02-29T05:53:03Z","abstract_excerpt":"The dynamics of the family of maps $\\displaystyle{f_{\\alpha, \\beta, \\gamma, \\delta}(z)=\\frac{\\alpha z + \\beta}{\\gamma z^2 +\\delta z}}$ in complex plane is investigated computationally. This dynamical system $z_{n+1}=f_{\\alpha, \\beta, \\gamma, \\delta}(z_n)=\\frac{\\alpha z_n + \\beta}{\\gamma z_n^2 +\\delta z_n}$ has periodic solutions with higher periods which was absent in the real line scenario. It is also found that there are chaotic fractal and non-fractal like solutions of the dynamical systems. A few special cases of parameters are also have been taken care."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00007","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"}