Working Paper Article Version 1 This version is not peer-reviewed

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.

Journal reference: Symmetry 2020, 12, 177
DOI: 10.3390/sym12010177

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.

Subject Areas

icosahedron; dynamics; equivariant map

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