SOME RESULTS ON BUNDLE SYSTEMS FOR A COUNTABLE DISCRETE AMENABLE GROUP ACTION*

doi:10.1007/s10473-023-0322-1

Abstract

Abstract: 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.

Key words: mean linear independence, style number, independence number, entropy

Juan Pan, Yunhua Zhou. SOME RESULTS ON BUNDLE SYSTEMS FOR A COUNTABLE DISCRETE AMENABLE GROUP ACTION^*[J].Acta mathematica scientia,Series B, 2023, 43(3): 1382-1402.

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SOME RESULTS ON BUNDLE SYSTEMS FOR A COUNTABLE DISCRETE AMENABLE GROUP ACTION^*

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