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

被引：0

作者：

Genovese, Giuseppe ^{[1
]}

Luca, Renato ^{[2
]}

Montalto, Riccardo ^{[3
]}

机构：

[1] Univ British Columbia, Dept Math, 228-1984 Math Rd, Vancouver, BC V6T 1Z2, Canada

[2] Univ Orleans, CNRS, Inst Denis Poisson, UMR 7013, Rue Chartres, F-45100 Orleans, France

[3] Univ Statale Milano, Dipartimento Matemat Federigo Enr, Via Saldini 50, I-20133 Milan, Italy

来源：

EMS SURVEYS IN MATHEMATICAL SCIENCES | 2025年 / 12卷 / 01期

关键词：

cubic Schr & ouml; dinger equations; Gibbs measure; quasi-invariance; Birkhoff normal form; NONLINEAR SCHRODINGER-EQUATION; KLEIN-GORDON EQUATION; LONG-TIME EXISTENCE; NORMAL-FORM;

D O I：

10.4171/EMSS/94

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Gibbs measure associated to the periodic cubic nonlinear Schr & ouml;dinger 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.

引用

页码：27 / 69

页数：43

共 31 条

[1] Almost Global Existence for Some Hamiltonian PDEs with Small Cauchy Data on General Tori [J].

Bambusi, D. ;

Feola, R. ;

Montalto, R. .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2024, 405 (01)

[2] Almost global existence for Hamiltonian semilinear Klein-Gordon equations with small Cauchy data on zoll manifolds [J].

Bambusi, D. ;

Delort, J.-M. ;

Grebert, B. ;

Szeftel, J. .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2007, 60 (11) :1665-1690

[3] Birkhoff normal form for partial differential equations with tame modulus [J].

Bambusi, D. ;

Grebert, B. .

DUKE MATHEMATICAL JOURNAL, 2006, 135 (03) :507-567

[4] Birkhoff normal form for some nonlinear PDEs [J].

Bambusi, D .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 234 (02) :253-285

[5]

Berti M., 2018, Almost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions

[6] Hamiltonian Birkhoff Normal Form for Gravity-Capillary Water Waves with Constant Vorticity: Almost Global Existence [J].

Berti, Massimiliano ;

Maspero, Alberto ;

Murgante, Federico .

ANNALS OF PDE, 2024, 10 (02)

[7] Birkhoff Normal Form and Long Time Existence for Periodic Gravity Water Waves [J].

Berti, Massimiliano ;

Feola, Roberto ;

Pusateri, Fabio .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2023, 76 (07) :1416-1494

[8] Construction of approximative and almost periodic solutions of perturbed linear Schrodinger and wave equations [J].

Bourgain, J .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 1996, 6 (02) :201-230

[9] PERIODIC NONLINEAR SCHRODINGER-EQUATION AND INVARIANT-MEASURES [J].

BOURGAIN, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 166 (01) :1-26

[10] Quasi-invariance of Gaussian measures transported by the cubic NLS with third-order dispersion on T [J].

Debussche, Arnaud ;

Tsutsumi, Yoshio .

JOURNAL OF FUNCTIONAL ANALYSIS, 2021, 281 (03)

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