Abstract
Motivated by an interpretation of the Fibonacci sequence as a subset of the free group F2 we describe orbits on finite subgroups of SU(2). A prerequisite for the calculation of these orbits is the knowledge of all generating sets of finite subgroups of SU(2). In order to facilitate this problem we introduce an equivalence relation between generating sets which can be extended to another one between Fibonacci orbits. Additionally, we describe a possible experiment with quasiperiodic dynamics.
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