Reductions related with Hopf maps

TL;DR

This paper explores reductions of high-dimensional particle systems linked to Hopf maps, explicitly constructing symmetry functions for the third Hopf map related to fiber rotations.

Contribution

It provides explicit constructions of symmetry functions for the third Hopf map in particle system reductions.

Findings

Explicit functions for third Hopf map symmetry constructed

Reductions for 2p-dimensional systems with p=2,4,8 analyzed

Connections between Hopf maps and particle system symmetries established

Abstract

We consider the reductions of $2p$-dimensional particle system ($p=2,4,8$), associated with the Hopf map. For the third Hopf map we explicitly construct the functions associated to the symmetry related to the rotations in the fiber.