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math.AP2023
KAM via Standard Fixed Point Theorems
Thomas Alazard, Chengyang Shao
With a mere usage of well-established properties of para-differential operators, the conjugacy equations in several model KAM problems are converted to para-homological equations s…
math.AP2023★ 2 cited
On the Cauchy Problem of Spherical Capillary Water Waves
Chengyang Shao
The spherical capillary water waves equation describes the motion of an almost spherical water droplet under zero gravity governed by water-air interface tension. Using para-differ…
math.AP2023★ 2 cited
Toolbox of Para-differential Calculus on Compact Lie Groups
Chengyang Shao
This paper provides a toolbox of para-differential calculus on compact Lie groups. The toolbox is based on representation theory of compact Lie groups and contains exact formulas o…