{"paper":{"title":"Dynamics of certain non-conformal degree two maps on the plane","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ben Bielefeld, Folkert Tangerman, J. J. P. Veerman, Scott Sutherland","submitted_at":"1991-09-26T00:00:00Z","abstract_excerpt":"In this paper we consider maps on the plane which are similar to quadratic maps in that they are degree 2 branched covers of the plane. In fact, consider for $\\alpha$ fixed, maps $f_c$ which have the following form (in polar coordinates):\n  $$f_c(r\\,e^{i\\theta})\\;=\\;r^{2\\alpha}\\,e^{2i\\theta}\\,+\\,c$$\n  When $\\alpha=1$, these maps are quadratic ($z \\maps z^2 + c$), and their dynamics and bifurcation theory are to some degree understood. When $\\alpha$ is different from one, the dynamics is no longer conformal. In particular, the dynamics is not completely determined by the orbit of the critical p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201293","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"}