Geodesic
Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map
Giuseppe Genovese1 orcid ; Renato Lucà2 orcid ; Riccardo Montalto3 orcid
1University of British Columbia, Vancouver, Canada
2Université d’Orléans, Orléans, France
3Universitá Statale di Milano, Milan, Italy
EMS surveys in mathematical sciences, Tome 12 (2025) no. 1, pp. 27-69

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DOI

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.
DOI : 10.4171/emss/94
Classification : 35Q55
Mots-clés : cubic Schrödinger equations, Gibbs measure, quasi-invariance, Birkhoff normal form

Giuseppe Genovese  1   ; Renato Lucà  2   ; Riccardo Montalto  3

1 University of British Columbia, Vancouver, Canada
2 Université d’Orléans, Orléans, France
3 Universitá Statale di Milano, Milan, Italy 
Giuseppe Genovese; Renato Lucà; Riccardo Montalto. Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map. EMS surveys in mathematical sciences, Tome 12 (2025) no. 1, pp. 27-69. doi: 10.4171/emss/94
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     title = {Transformation of the {Gibbs} measure of the cubic {NLS} and fractional {NLS} under an approximated {Birkhoff} map},
     journal = {EMS surveys in mathematical sciences},
     pages = {27--69},
     year = {2025},
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     number = {1},
     doi = {10.4171/emss/94},
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