23 citations · 192 across the 39 of their papers we have counts for
39 papers
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…
Ergodic Optimization Restricted On Certain Subsets Of Invariant Measures
Wanshan Lin, Xueting Tian
In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems,…
Uniqueness Of Ergodic Optimization Of Top Lyapunov Exponent For Typical Matrix Cocycles
Wanshan Lin, Xueting Tian
In this article, we consider the ergodic optimization of the top Lyapunov exponent. We prove that there is a unique maximising measure of top Lyapunov expoent for typical matrix co…
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…
On multifractal analysis and large deviations of singular-hyperbolic attractors
Yi Shi, Xueting Tian, Paulo Varandas +1
In this paper we study the multifractal analysis and large derivations for singular hyperbolic attractors, including the geometric Lorenz attractors. For each singular hyperbolic h…
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…
On the topological entropy of saturated sets for amenable group actions
Xiankun Ren, Xueting Tian, Yunhua zhou
Let be a action topological system, where is a countable infinite discrete amenable group and a compact metric space. We prove a variational principle for top…
A -connecting lemma for Lorenz attractors and its application on the space of ergodic measures
Yi Shi, Xueting Tian, Xiaodong Wang
For every , we prove a -connecting lemma for Lorenz attractors. To be precise, for a Lorenz attractor of a -dimensional ($r\geq…
Existence and Distributional Chaos of Points that are Recurrent but Not Banach Recurrent
Yifan Jiang, Xueting Tian
According to the recurrent frequency, many levels of recurrent points are found, such as periodic points, almost periodic points, weakly almost periodic points, quasi-weakly almost…
Physical-like Measures Coincide with Invariant Measures Supported on Chain Recurrent Classes
Xueting Tian
For generic continuous maps or homeomorphisms on compact Riemannian manifold, we prove that (1) the space of physical-like measures coincides with the set of invariant measur…
Laypunov Irregular Points With Distributional Chaos
An Chen, Xueting Tian
It follows from Oseledec Multiplicative Ergodic Theorem (or Kingmans Subadditional Ergodic Theorem) that the Lyapunov-irregular set of points for which the Oseledec averages of a g…
Unstable entropies and Dimension Theory of Partially Hyperbolic Systems
Xueting Tian, Weisheng Wu
In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carathéodory dimension characterist…
Distributional chaos in multifractal analysis, recurrence and transitivity
An Chen, Xueting Tian
There are lots of results to study dynamical complexity on irregular sets and level sets of ergodic average from the perspective of density in base space, Hausdorff dimension, Lebe…
Different Statistical Future of Dynamical Orbits over Expanding or Hyperbolic Systems (II): Nonempty Syndetic Center
Yiwei Dong, Xueting Tian
In [30] different statistical behavior of dynamical orbits without syndetic center are considered. In present paper we continue this project and consider different statistical beha…
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…
Transitively-Saturated Property, Banach Recurrence and Lyapunov Regularity
Yu Huang, Xueting Tian, Xiaoyi Wang
The topological entropy of various gap-sets on periodic-like recurrence and Birkhoff regularity were considered in [69] but some Banach recurrence and Lyapunov regularity are not c…
Topological Entropy on Points without Physical-like Behaviour
Eleonora Catsigeras, Xueting Tian, Edson Vargas
We study a class of asymptotically entropy-expansive diffeomorphisms with dominated splitting on a compact manifold , that satisfy the specification property. This class i…
Multifractal Analysis of The New Level Sets
Yiwei Dong, Xueting Tian
By an appropriate definition, we divide the irregular set into level sets. Then we characterize the multifractal spectrum of these new pieces by calculating their entropies. We als…
On the irregular points for systems with the shadowing property
Yiwei Dong, Piotr Oprocha, Xueting Tian
We prove that when is a continuous selfmap acting on compact metric space which satisfies the shadowing property, then the set of irregular points (i.e. points with div…
Nonexistence of Lyapunov Exponents for Matrix Cocycles
Xueting Tian
It follows from Oseledec Multiplicative Ergodic Theorem that the Lyapunov-irregular set of points for which the Oseledec averages of a given continuous cocycle diverge has zero mea…