Article
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Critically-Finite Dynamics on the Icosahedron
Version 1
: Received: 11 December 2019 / Approved: 15 December 2019 / Online: 15 December 2019 (13:31:39 CET)
A peer-reviewed article of this Preprint also exists.
Crass, S. Critically-Finite Dynamics on the Icosahedron. Symmetry 2020, 12, 177. Crass, S. Critically-Finite Dynamics on the Icosahedron. Symmetry 2020, 12, 177.
Abstract
Drawing inspiration from a recent construction of a polyhedral structure associated with an icosahedrally-symmetric map on the Riemann sphere, the article shows how to build such "dynamical polyhedra" for other icosahedral maps. First, icosahedral algebra is used to determine a special family of maps with 60 periodic critical points. The topological behavior of each map is worked out and results in a geometric algorithm that constructs a system of edges---the dynamical polyhedron---in natural correspondence to a map's topology. It turns out that the maps' descriptions fall into classes the presentation of which concludes the paper.
Keywords
icosahedron; dynamics; equivariant map
Subject
Computer Science and Mathematics, Computer Science
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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