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math.DS2019
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…
math.DS2019
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…
math.DS2019
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…