Variational principles on r -neutralized dimensions and entropies
Xiaoyu Zhang, Yunxiang Xie
Source abstract
Using r-neutralized Bowen balls, we introduce the r-neutralized Barreira-Schmeling (BS)-packing dimension and r-neutralized packing topological pressure for subsets. In the spirit of the classical Brin-Katok local entropy formula, we define three measure-theoretic quantities and prove a variational principle that is closely related to the r-neutralized BS-packing dimension. Furthermore, we prove that r-neutralized BS-packing dimension serves as the unique root of the corresponding Bowen’s equation. Additionally, we investigate further structural properties involving various r-neutralized entropies.
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