9 papers
Topological entropy of saturated sets for Lorenz attractors
Zheng Huang, Xueting Tian, Xiaodong Wang +1
We study the topological entropy of saturated sets for continuous flows, with emphasis on singular hyperbolic dynamics. For a -generic () vector field carrying a…
Realizing prescribed entropy functions by smooth diffeomorphisms of closed manifolds of dimension at least three
Wanshan Lin, Xueting Tian
Let be a closed smooth manifold of dimension . Given a compact metrizable Choquet simplex and a bounded nonnegative affine upper semicontinuous function $\…
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…
On the loss of upper semi-continuity of metric entropy for diffeomorphisms
Xinyu Bai, Wanshan Lin, Xueting Tian
In this article, we give an upper bound estimate for the quantitative loss of upper semicontinuity of metric entropy for diffeomorphisms. Building on earlier entropy e…
Variations of topological theory and ergodic theory via gap function in non-uniform specification
Wanshan Lin, Xueting Tian, Chenwei Yu
In our previous work [43], we studied qualitative differences between specification and nonuniform specification. In this paper, we investigate quantitative variations depending on…
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…
Non-uniform Cocycles for Some Uniquely Ergodic Minimal Dynamical Systems on Connected Spaces
Wanshan Lin, Xueting Tian
In this paper, we pay attention to a weaker version of Walters's question on the existence of non-uniform cocycles for uniquely ergodic minimal dynamical systems on non-degenerate…