Crass, S. Critically-Finite Dynamics on the Icosahedron. Symmetry2020, 12, 177.
Crass, S. Critically-Finite Dynamics on the Icosahedron. Symmetry 2020, 12, 177.
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.
icosahedron; dynamics; equivariant map
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.