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math.DS2022★ 1 cited
Invariant tori for area-preserving maps with ultra-differentiable perturbation and Liouvillean frequency
Hongyu Cheng, Shimin Wang, Fenfen Wang
We prove the existence of invariant tori to the area-preserving maps defined on \begin{equation*} \bar{x}=F(x,θ), \qquad \barθ=θ+α\, \,(α\in \mathb…
math.DS2021★ 1 cited
Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications
Hongyu Cheng, Lingrui Ge, Jiangong You +1
For quasiperiodic Schrödinger operators with one-frequency analytic potentials, from dynamical systems side, it has been proved that the corresponding quasiperiodic Schrödinger coc…
math.DS2019★ 1 cited
Response solutions to the quasi-periodically forced systems with degenerate equilibrium: A simple proof of a result of W. Si and J. Si. and extensions
Hongyu Cheng, Rafael de la Llave, Fenfen Wang
We give a simple proof of the existence of response solutions in some quasi-periodically forced systems with a degenerate fixed points. The same questions were answered in \cite{ss…