We study the Gibbs measure associated to the periodic cubic nonlinear Schrodinger 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.
Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map / G. Genovese, R. Luca, R. Montalto. - In: EMS SURVEYS IN MATHEMATICAL SCIENCES. - ISSN 2308-2151. - 12:1(2025), pp. 27-69. [10.4171/EMSS/94]
Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map
R. MontaltoUltimo
2025
Abstract
We study the Gibbs measure associated to the periodic cubic nonlinear Schrodinger 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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