The variational principle of topological pressure for actions of sofic groupoids
This article establishes the variational principle of topological pressure for actions of sofic groupoids.
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arXiv subjects
Xiaoyao Zhou
Publications and source records attributed to Xiaoyao Zhou.
Multifractal analysis for historic set in topological dynamical systems
In this article, the historic set is divided into different level sets and we use topological pressure to describe the size of these level sets. We give an application of these results to dimension theory. Especially, we use topological pressure to describe the relative multifractal spectrum of ergodic averages and give a positive answer to the conjecture posed by L. Olsen (J. Math. Pures Appl. {\bf 82} (2003)).
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Packing dimensions of the divergence points of self-similar measures with the open set condition
Let $μ$ be the self-similar measure supported on the self-similar set $K$ with open set condition. In this article, we discuss the packing dimension of the set $\{x\in K: A(\frac{\logμ(B(x,r))}{\log r})=I\}$ for $I\subseteq\mathbb{R}$, where $A(\frac{\logμ(B(x,r))}{\log r})$ denotes the set of accumulation points of \frac{\logμ(B(x,r))}{\log r}$ as $r\searrow0$. Our main result solves the conjecture about packing dimension posed by Olsen and Winter \cite{OlsWin} and generalizes the result in \cite{BaeOlsSni}.
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The variational principle of local pressure for actions of sofic group
This study establishes the variational principle for local pressure in the sofic context.
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