Antipode preserving cubic maps: the Fjord theorem. Issue 3 (10th January 2018)

• Record Type: Journal Article
• Authors: Bonifant, Araceli; Buff, Xavier; Milnor, John
• Is Part Of: Proceedings of the London Mathematical Society. Volume 116:Issue 3(2018)
• Page Start: 670
• Page End: 728
• Publication Date: 2018-01-10
• Subjects: 37D05 -- 37F10 (primary) -- 37F15 -- 37D05 -- 32A10 -- 32H02 (secondary); Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms.12075
• Languages: English
• ISSNs: 0024-6115

Abstract

Abstract: This note will study a family of cubic rational maps which carry antipodal points of the Riemann sphere to antipodal points. It focuses particularly on the fjords, which are part of the central hyperbolic component but stretch out to infinity. These serve to decompose the parameter plane into subsets, each of which is characterized by a corresponding rotation number .