Invariant Varieties of Periodic Points for the Discrete Euler Top

TL;DR

This paper investigates the periodic points of the discrete Euler top, explicitly deriving invariant varieties and showing how symmetry influences these points based on angular velocity values.

Contribution

It provides explicit derivations of invariant varieties of periodic points for the discrete Euler top, especially highlighting the symmetric case.

Findings

Invariant varieties of periodic points are explicitly derived.

Symmetry simplifies the characterization of periodic points.

Periodic points depend on specific angular velocity values.

Abstract

The behaviour of periodic points of discrete Euler top is studied. We derive invariant varieties of periodic points explicitly. When the top is axially symmetric they are specified by some particular values of the angular velocity along the axis of symmetry, different for each period.