Ergodic measures of intermediate entropies for amenable group actions with an approximate product property
Year: 2026
Type: preprint
Abstract: We study entropy realization for continuous actions of infinite countable amenable groups. We introduce an approximate product property for amenable group actions that permits a small proportion of tracing mistakes on prescribed pairwise disjoint, sufficiently invariant finite sets. We prove that this property implies entropy-denseness and almost entropy-approximability of every invariant measure. The construction combines zero-entropy exact tilings with a finite-block estimate for the complexity of tracing mistakes. Under asymptotic entropy expansiveness, almost entropy-approximability upgrades to entropy-approximability. For every $0\leqα
Source: arXiv (Cornell University)
Authors: Zhang, Wenda, Ren, Xiankun
Institutions: Chongqing University, Chongqing Jiaotong University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G6892761941, G8896436568
OpenAlex ID: W7220934550