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math.DS2022
Relation between irrationality and regularity for conjugacy of circle diffeomorphisms to rigid rotations
Zhicheng Tong, Shuyuan Xiao, Yong Li
By introducing the modulus of continuity, we first establish the corresponding cross-ratio distortion estimates under smoothness, and further derive a Denjoy-type inequalit…
math.DS2022★ 7 cited
KAM theorem on modulus of continuity about parameter
Zhicheng Tong, Jiayin Du, Yong Li
In this paper, we study the Hamiltonian systems $ H\left( {y,x,ξ,\varepsilon } \right) = \left\langle {ω\left( ξ\right),y} \right\rangle + \varepsilon P\left( {y,x,ξ,\varepsilon }…
math.DS2022★ 16 cited
Exponential convergence of weighted Birkhoff average
Zhicheng Tong, Yong Li
In this paper, we consider the polynomial and exponential convergence rate of weighted Birkhoff averages of irrational rotations on tori. It is shown that these can be achieved for…