6 papers · 1 filter
Conditional entropy realization and approximation by uniquely ergodic measures
Xiaobo Hou, Wanshan Lin, Xueting Tian +2
This paper studies conditional entropy realization and weak* approximation by uniquely ergodic measures with compact support. We prove that, after fixing an admissible potential av…
Analytic Paths of Ergodic Measures with Prescribed Invariants
Xiaobo Hou, Xueting Tian
We study analytic paths of ergodic measures under quantitative constraints. For uniformly hyperbolic systems, we construct one-parameter families of ergodic measures whose prescrib…
Complete realization of multifractal entropy spectra and pressure functions
Xiaobo Hou, Xueting Tian, Wanshan Lin
We give a complete characterization of the multifractal entropy spectra arising from continuous vector-valued potentials on transitive two-sided shifts of finite type. We prove tha…
Bohr chaoticity, semi-horseshoes and full-entropy abundance
Xiaobo Hou, Wanshan Lin, Xueting Tian
Bohr chaoticity is a topological notion of dynamical complexity defined through non-orthogonality to all non-trivial weights. It is strictly stronger than positivity of topological…
Different Statistical Behaviors of Orbits
Yiwei Dong, Xiaobo Hou, Wanshan Lin +1
In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, t…
Topological entropy and Hausdorff dimension of shrinking target sets
Xiaobo Hou, Xueting Tian, Yiwei Zhang
In this paper, we study the topological entropy and the Hausdorff dimension of a shrinking target set. We give lower and upper bounds of topological entropy and Hausdorff dimension…