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Uniform Diophantine approximation related to beta-transformations
Wanlou Wu
For any , let be the classical -transformations. Fix and a nonnegative real number , we compute the Hausdorff dimension of the set of real numb…
Dimension theory of Diophantine approximation related to -transformations
Wanlou Wu, Lixuan Zheng
Let be the -transformation on defined by We study the Diophantine approximation of the orbit of a point under . Precisely, for…
Approximation property on entropies for surface diffeomorphisms
Wanlou Wu, Jiansong Liu
In this paper, we prove that for any surface diffeomorphism with positive topological entropy, there exists a diffeomorphism arbitrarily close (in the topology)…
On the F-expanding of Homoclinic class
Wanlou Wu, Bo Li
We establish a closing property for thin trapped homoclinic classes. Taking advantage of this property, we proved that if the homoclinic class admits a dominated splitting $…
On the growth rate of periodic orbits for vector fields
Wanlou Wu, Dawei Yang, Yong Zhang
We establish the relationship between the growth rate of periodic orbits and the topological entropy for generic vector fields: this extends a classical result of Katok for $…