# A separation lemma on sub-lattices

@inproceedings{Wang2021ASL, title={A separation lemma on sub-lattices}, author={W.-M. Wang}, year={2021} }

We prove that Bourgain’s separation lemma, Lemma 20.14 [B2] holds at fixed frequencies and their neighborhoods, on sub-lattices, sub-modules of the dual lattice associated with a quasi-periodic Fourier series in two dimensions. And by extension holds on the affine spaces. Previously Bourgain’s lemma was not deterministic, and is valid only for a set of frequencies of positive measure. The new separation lemma generalizes classical lattice partition-type results to the hyperbolic Lorentzian…

## One Citation

A P ] 2 J un 2 02 1 QUASI-PERIODIC SOLUTIONS TO A NONLINEAR KLEIN-GORDON EQUATION WITH A DECAYING NONLINEAR TERM

- 2021

We present a set of time quasi-periodic solutions to a nonlinear KleinGordon equation with a decaying nonlinear term on the torus in arbitrary dimensions. This generalizes the bifurcation method…

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A P ] 2 J un 2 02 1 QUASI-PERIODIC SOLUTIONS TO A NONLINEAR KLEIN-GORDON EQUATION WITH A DECAYING NONLINEAR TERM

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We present a set of time quasi-periodic solutions to a nonlinear KleinGordon equation with a decaying nonlinear term on the torus in arbitrary dimensions. This generalizes the bifurcation method…

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