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About linearization of infinite-dimensional Hamiltonian systems (Q2160227)

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Language	Label	Description	Also known as
English	About linearization of infinite-dimensional Hamiltonian systems	scientific article

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scholarly article

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About linearization of infinite-dimensional Hamiltonian systems (English)

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Laurent Stolovitch

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Michela Procesi

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Communications in Mathematical Physics

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publication date

3 August 2022

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full work available at URL

https://arxiv.org/abs/2108.00060

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zbMATH Keywords

analytic Hamiltonian dynamical systems

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Birkhoff normal form

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Gevrey regularity

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MaRDI profile type

MaRDI publication profile

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Time quasi-periodic gravity water waves in finite depth

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Nekhoroshev theorem for small amplitude solutions in nonlinear Schrödinger equations

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On long time stability in Hamiltonian perturbations of non-resonant linear PDEs

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Birkhoff normal form for some nonlinear PDEs

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Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds

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Forme normale pour NLS en dimension quelconque. (Normal form for NLS in arbitrary dimension)

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Birkhoff normal form for partial differential equations with tame modulus

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Convergence to normal forms of integrable PDEs

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The steep Nekhoroshev's theorem

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A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems

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A Nekhoroshev-type theorem for Hamiltonian systems with infinitely many degrees of freedom

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KAM theory for the Hamiltonian derivative wave equation

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Quasi-periodic solutions of nonlinear wave equations on the \(d\)-dimensional torus

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An abstract Nash-Moser theorem with parameters and applications to PDEs

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An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifolds

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Birkhoff normal form for gravity water waves

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Almost global solutions of capillary-gravity water waves equations on the circle

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Traveling quasi-periodic water waves with constant vorticity

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An abstract Birkhoff normal form theorem and exponential type stability of the 1d NLS

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Almost periodic invariant tori for the NLS on the circle

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Super-exponential stability for generic real-analytic elliptic equilibrium points

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Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations

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Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations

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On invariant tori of full dimension for 1D periodic NLS

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Quasi-periodic solutions for the forced Kirchhoff equation on $ \newcommand{\m}{\mu} \newcommand{\T}{\mathbb T} \T^d$

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The stability of full dimensional KAM tori for nonlinear Schrödinger equation

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A Nekhoroshev type theorem for the derivative nonlinear Schrödinger equation

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The existence of full dimensional invariant tori for 1-dimensional nonlinear wave equation

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Newton's method and periodic solutions of nonlinear wave equations

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Bounded almost global solutions for non Hamiltonian semi-linear Klein-Gordon equations with radial data on compact revolution hypersurfaces

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Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres

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KAM for the nonlinear Schrödinger equation

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A Nekhoroshev-type theorem for the nonlinear Schrödinger equation on the torus

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Time quasi-periodic traveling gravity water waves in infinite depth

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On the integrability of Degasperis-Procesi equation: control of the Sobolev norms and Birkhoff resonances

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Reducible KAM tori for the Degasperis-Procesi equation

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Long time existence for fully nonlinear NLS with small Cauchy data on the circle

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An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation

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Polynomial normal forms with exponentially small remainder for analytic vector fields

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Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation

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Normal forms of analytic perturbations of quasihomogeneous vector fields: Rigidity, invariant analytic sets and exponentially small approximation

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Exponential stability for small perturbations of steep integrable Hamiltonian systems

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The method of Poincaré normal forms in problems of integrability of equations of evolution type

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Small divisors with spatial structure in infinite dimensional Hamiltonian systems

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On invariant manifolds of complex analytic mappings near fixed points

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Reducible quasi-periodic solutions for the non linear Schrödinger equation

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Lie algebras and Lie groups. 1964 lectures, given at Harvard University.

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Iteration of analytic functions

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Singular complete integrability

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Family of intersecting totally real manifolds of $(C^n ,0)$ and germs of holomorphic diffeomorphisms

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Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory

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<scp>KAM</scp> Theorem with Normal Frequencies of Finite <scp>Limit‐Points</scp> for Some Shallow Water Equations

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Long Time Stability of Hamiltonian Partial Differential Equations

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C. L. Siegel's linearization theorem in infinite dimensions

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Identifiers

zbMATH Open document ID

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10.1007/s00220-022-04398-7

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

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