Some Results on Bundle Systems for a Countable Discrete Amenable Group Action

We consider the style number, independence number and entropy for a frame bundle dynamical system. The base system of which is a countable discrete amenable group action on a compact metric space. We obtain the existence of cover measures, an ergodic theorem about mean linear independence and the style number, and a variational principle for style numbers and independence numbers. We also study the relationship between the entropy of base systems and that of their bundle systems.

Automated summary

In this paper, we investigate the style number, independence number, and entropy of a frame bundle dynamical system. The base system is a countable discrete amenable group action on a compact metric space. We establish the existence of cover measures, an ergodic theorem concerning mean linear independence and the style number, and a variational principle for style numbers and independence numbers. Furthermore, we examine the relationship between the entropy of base systems and that of their bundle systems.