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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.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…
math.DS2019★ 2 cited
Response solutions to quasi-periodically forced systems, even to possibly ill-posed PDEs, with strong dissipation and any frequency vectors
Fenfen Wang, Rafael de la Llave
We consider several models (including both multidimensional ordinary differential equations (ODEs) and partial differential equations (PDEs), possibly ill-posed), subject to very s…