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Antipode preserving cubic maps: the Fjord theorem
Author(s) -
Bonifant Araceli,
Buff Xavier,
Milnor John
Publication year - 2018
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12075
Subject(s) - mathematics , fjord , pure mathematics , combinatorics , geology , oceanography
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 .