3 citations · 8 across the 13 of their papers we have counts for
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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…
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…
Complete realization of multifractal entropy spectra and pressure functions
Xiaobo Hou, Wanshan Lin, Xueting Tian
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…
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…
Conditional intermediate entropy and Birkhoff average properties of hyperbolic flows
Xiaobo Hou, Xueting Tian
Katok conjectured that every diffeomorphism on a Riemannian manifold has the intermediate entropy property, that is, for any constant , there exis…
Abundance of Smale's horseshoes and ergodic measures via multifractal analysis and various quantitative spectrums
Yiwei Dong, Xiaobo Hou, Xueting Tian
In this article, we combine the perspectives of density, entropy, and multifractal analysis to investigate the structure of ergodic measures. We prove that for each transitive topo…
Strongly distributional chaos in the sets of twelve different types of non-recurrent points
An Chen, Xiaobo Hou, Wanshan Lin +1
In present paper we mainly focus on non-recurrent dynamical orbits with empty syndetic center and show that twelve different statistical structures over mixing expanding maps or tr…
Entropy of irregular points that are not uniformly hyperbolic
Xiaobo Hou, Xueting Tian
In this article we prove that for a diffeomorphism on a compact Riemannian manifold, if there is a hyperbolic ergodic measure whose support is not uniformly hyperbolic, t…
Strongly distributional chaos of irregular orbits that are not uniformly hyperbolic
Xiaobo Hou, Xueting Tian
In this article we prove that for a diffeomorphism on a compact Riemannian manifold, if there is a nontrival homoclinic class that is not uniformly hyperbolic or the diffeomorphism…
Ergodic Average Of Typical Orbits And Typical Functions
Xiaobo Hou, Wanshan Lin, Xueting Tian
In this article we mainly aim to know what kind of asymptotic behavior of typical orbits can display. For example, we show in any transitive system, the emprical measures of a typi…
Topological structures on saturated sets, optimal orbits and equilibrium states
Xiaobo Hou, Xueting Tian, Yiwei Zhang
Pfister and Sullivan proved that if a topological dynamical system satisfies almost product property and uniform separation property, then for each nonempty compact %convex…
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…