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 existe...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.展开更多
基金supported by the Natural Science Foundation of China(11871120, 12071082)the Natural Science Foundation of Chongqing (cstc2021jcyj-msxm X0299)。
文摘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.
