JournalsemssVol. 12, No. 1pp. 27–69

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

  • Giuseppe Genovese

    University of British Columbia, Vancouver, Canada
    ORCID

  • Renato Lucà

    Université d’Orléans, Orléans, France
    ORCID

  • Riccardo Montalto

    Universitá Statale di Milano, Milan, Italy
    ORCID
Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map cover
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Abstract

We study the Gibbs measure associated to the periodic cubic nonlinear Schrödinger 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.

Cite this article

Giuseppe Genovese, Renato Lucà, Riccardo Montalto, Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map. EMS Surv. Math. Sci. 12 (2025), no. 1, pp. 27–69

DOI 10.4171/EMSS/94