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arXiv · 2312.09795

Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map

Giuseppe Genovese·Renato Lucà·Riccardo Montalto
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Abstract

We study the Gibbs measure associated to the periodic cubic nonlinear Schr\"odinger equation. We establish a change of variable formula for this measure under the first step of the Birkhoff normal form reduction. We also consider the case of fractional dispersion.

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Giuseppe Genovese, Renato Lucà, Riccardo Montalto. 2023-12-15. Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map. https://arxiv.org/abs/2312.09795

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