arXiv subjects
Publications and source records attributed to Cao Zhao.
Let $(X,d,T )$ be a topological dynamical system with the specification property. We consider the non-dense orbit set $E(z_0)$ and show that for any non-transitive point $z_0\in X$, this set $E(z_0)$ is empty or carries full topological pressure.
Let $(X,d,T )$ be a topological dynamical system with specification property. For $ α\in \mathbb R^+$ and any $x_0\in X$, define $$ \mathbf D^{x_0}_α:=\Big\{x\in X: \lim\limits_{ε\to 0}\limsup\limits_{n\to\infty}\dfrac{\max\{t\in\mathbb N:~T^n(x)\in B_{t}( x_0,ε)\}}{n}\geq α\Big\}.$$ Then we have $h_{top}^{B} ( T, \mathbf D^{x_0}_α)= \dfrac{h_{top}(T)}{1+α} $, where $h_{top}^{B} ( T, \mathbf D^{x_0}_α)$ denotes the Bowen topological entropy of $\mathbf D^{x_0}_α.$
We derive a conditional variational principle of the saturated set for systems with the non-uniform structure. Our result applies to a broad class of systems including beta-shifts, S-gap shifts and their factors.
Let X be a subshift satisfy non-uniform structure. In this paper, we give quantitative estimate of the recurrence sets. These results can be applied to a large class of symbolic systems, including beta-shifts, S-gap shifts and their factors.