Nearly integrable infinite-dimensional Hamiltonian systems
From MaRDI portal
Publication:1310301
DOI10.1007/BFb0092243zbMath0784.58028MaRDI QIDQ1310301
Publication date: 12 December 1993
Published in: Lecture Notes in Mathematics (Search for Journal in Brave)
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Partial differential equations (35-XX)
Related Items
Quasi-periodic solutions of two dimensional Schrödinger equations with quasi-periodic forcing ⋮ Quasi-periodic solutions for fractional nonlinear Schrödinger equation ⋮ Gevrey-smoothness of elliptic lower dimensional invariant tori in Hamiltonian systems ⋮ Persistence of lower dimensional hyperbolic tori for reversible system ⋮ Moser's theorem for lower dimensional tori ⋮ KAM for the Klein Gordon equation on \(\mathbb {S}^d\) ⋮ Two-dimensional invariant tori in the neighborhood of an elliptic equilibrium of Hamiltonian systems ⋮ Reducibility of first order linear operators on tori via Moser's theorem ⋮ Infinite-dimensional symplectic capacities and a squeezing theorem for Hamiltonian PDE's ⋮ Small-amplitude solutions of the sine-Gordon equation on an interval under Dirichlet or Neumann boundary conditions ⋮ Construction of periodic solutions of nonlinear wave equations in higher dimension ⋮ On squeezing and flow of energy for nonlinear wave equations ⋮ Persistence of the hyperbolic lower dimensional non-twist invariant torus in a class of Hamiltonian systems ⋮ Smooth quasi-periodic solutions for the perturbed mKdV equation ⋮ A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces ⋮ Aspects of long time behaviour of solutions of nonlinear Hamiltonian evolution equations ⋮ Quasi-periodic solutions of completely resonant nonlinear wave equations ⋮ Persistence of elliptic lower dimensional invariant tori for small perturbation of degenerate integrable Hamiltonian systems ⋮ Quasi-periodic solutions for quasi-periodically forced nonlinear Schrödinger equations with quasi-periodic inhomogeneous terms ⋮ Birkhoff normal form for partial differential equations with tame modulus ⋮ Small-divisor equation of higher order with large variable coefficient and application to the coupled KdV equation ⋮ Nonlinear vibrations of a beam with time-varying rigidity and mass ⋮ Non-Floquet invariant tori in reversible systems ⋮ Compensations in small divisor problems ⋮ Quasi-periodic solutions in a nonlinear Schrödinger equation ⋮ Existence and stability of quasi-periodic breathers in networks of Ginzburg--Landau oscillators ⋮ Lower dimensional invariant tori with prescribed frequency for nonlinear wave equation ⋮ Gevrey-smoothness of invariant tori for analytic nearly integrable Hamiltonian systems under Rüssmann's non-degeneracy condition ⋮ Growth and oscillations of solutions of nonlinear Schrödinger equation ⋮ Reducibility of the quantum harmonic oscillator in \(d\)-dimensions with polynomial time-dependent perturbation ⋮ Quasi-periodic solutions of derivative nonlinear Schrödinger equations with a given potential ⋮ How many first integrals imply integrability in infinite-dimensional Hamilton system ⋮ Invariant tori of full dimension for second KdV equations with the external parameters ⋮ Quasi-periodic solutions of a non-autonomous wave equations with quasi-periodic forcing ⋮ Degenerate KAM theory for partial differential equations ⋮ An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation ⋮ Periodic solutions for one dimensional wave equation with bounded nonlinearity ⋮ Quasi-periodic solutions of a quasi-periodically forced nonlinear beam equation ⋮ Forme normale pour NLS en dimension quelconque. (Normal form for NLS in arbitrary dimension) ⋮ Quasi-periodic solutions of nonlinear Schrödinger equations of higher dimension. ⋮ An a posteriori KAM theorem for whiskered tori in Hamiltonian partial differential equations with applications to some ill-posed equations ⋮ The almost-periodic solutions of the weakly coupled pendulum equations ⋮ KAM for the quantum harmonic oscillator ⋮ Invariant tori of full dimension for a nonlinear Schrödinger equation ⋮ Non-degeneracy conditions in KAM theory ⋮ Quasi-periodic solutions for 1D wave equation with higher order nonlinearity ⋮ On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces ⋮ Kolmogorov's theorem for low-dimensional invariant tori of Hamiltonian systems ⋮ Linearly stable quasi-periodic breathers in a class of random Hamiltonian systems ⋮ KAM theorems and open problems for infinite-dimensional Hamiltonian with short range ⋮ Analytic intermediate dimensional elliptic tori for the planetary many-body problem ⋮ Small-divisor equation with large-variable coefficient and periodic solutions of DNLS equations ⋮ Quasi-periodic solutions with prescribed frequency in reversible systems ⋮ Pure point spectrum of the Floquet Hamiltonian for the quantum harmonic oscillator under time quasi-periodic perturbations ⋮ Completely degenerate lower-dimensional invariant tori for Hamiltonian system ⋮ On Landau damping ⋮ Reducibility of one-dimensional quasi-periodic Schrödinger equations ⋮ KAM Tori for higher dimensional quintic beam equation ⋮ Construction of response solutions for two classes of quasi-periodically forced four-dimensional nonlinear systems with degenerate equilibrium point under small perturbations ⋮ KAM tori for quintic nonlinear Schrödinger equations with given potential ⋮ On lower dimensional invariant tori in \(C^d\) reversible systems ⋮ Reducibility, Lyapunov exponent, pure point spectra property for quasi-periodic wave operator ⋮ The stability of full dimensional KAM tori for nonlinear Schrödinger equation ⋮ On reducibility of 1d wave equation with quasiperiodic in time potentials ⋮ A KAM theorem for higher dimensional forced nonlinear Schrödinger equations ⋮ Quasi-periodic solutions of generalized Boussinesq equation with quasi-periodic forcing ⋮ A KAM theorem for space-multidimensional Hamiltonian PDEs ⋮ Quasi-periodic solutions for perturbed generalized nonlinear vibrating string equation with singularities ⋮ Reducibility of 1-d Schrödinger equation with time quasiperiodic unbounded perturbations. II ⋮ A Nekhoroshev type theorem for the nonlinear wave equation in Gevrey space ⋮ Perturbation theory for infinite-dimensional integrable systems on the line. A case study ⋮ Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation ⋮ A Birkhoff-Lewis type theorem for the nonlinear wave equation ⋮ Reducibility of relativistic Schrödinger equation with unbounded perturbations ⋮ Time-periodic solutions to the one-dimensional nonlinear wave equation ⋮ Periodic solutions for completely resonant nonlinear wave equations with Dirichlet boundary conditions ⋮ Quasi-periodic solutions for two dimensional modified Boussinesq equation ⋮ KAM for the nonlinear Schrödinger equation ⋮ Invariant tori of a nonlinear Schrödinger equation with quasi-periodically unbounded perturbations ⋮ Quasi-periodic solutions for nonlinear wave equation with Liouvillean frequency ⋮ KAM for the nonlinear beam equation ⋮ Moser's theorem for hyperbolic-type degenerate lower tori in Hamiltonian system ⋮ A KAM theorem for the Hamiltonian with finite zero normal frequencies and its applications (in memory of Professor Walter Craig) ⋮ Invariant tori of nonlinear Schrödinger equation ⋮ The quasi-periodic centre-saddle bifurcation ⋮ Quasi-periodic solutions for the generalized Benjamin-Bona-Mahony equation ⋮ Construction of quasi-periodic solutions of delay differential equations via KAM techniques ⋮ On the periodic KdV equation in weighted Sobolev spaces ⋮ Quasi-periodic solutions for perturbed autonomous delay differential equations ⋮ Almost periodic solutions for a class of higher dimensional Schrödinger equations ⋮ Perturbations of lower dimensional tori for Hamiltonian systems ⋮ Bifurcation of periodics and subharmonics in abstract nonlinear undamped wave equations ⋮ On long time existence for small solutions of semi-linear Klein-Gordon equations on the torus ⋮ Almost global solutions to Hamiltonian derivative nonlinear Schrödinger equations on the circle ⋮ Normal forms for semilinear quantum harmonic oscillators ⋮ Invariant tori for a two-dimensional completely resonant beam equation with a quintic nonlinear term ⋮ Persistence of lower dimensional invariant tori for nearly integrable Hamiltonian systems ⋮ Persistence of lower-dimensional tori under the first Melnikov's non-resonance condition ⋮ KAM tori of Hamiltonian perturbations of 1D linear beam equations ⋮ Breathers on a background: Periodic and quasiperiodic solutions of extended discrete nonlinear wave systems ⋮ A KAM algorithm for two-dimensional nonlinear Schrödinger equations with spatial variable ⋮ Quasi-periodic solutions for quintic completely resonant derivative beam equations on T2 ⋮ Quasi-periodic solution of quasi-linear fifth-order KdV equation ⋮ Quasi-periodic solutions for a generalized higher-order Boussinesq equation ⋮ The stability of Sobolev norms for the linear wave equation with unbounded perturbations ⋮ Quasi-periodic Solutions for Schrödinger Equation with Finite Smooth Quasi-periodic Forcing ⋮ Quasiperiodic Poincaré persistence at high degeneracy ⋮ Almost reducibility and oscillatory growth of Sobolev norms ⋮ On lower dimensional invariant tori in reversible systems ⋮ Persistence of lower dimensional tori of general types in Hamiltonian systems ⋮ Degenerate response tori in Hamiltonian systems with higher zero-average perturbation ⋮ Reducibility of beam equations in higher-dimensional spaces ⋮ Periodic solutions of two-dimensional wave equations with x-dependent coefficients and Sturm–Liouville boundary conditions ⋮ Quasi-periodic solutions for one dimensional Schrödinger equation with quasi-periodic forcing and Dirichlet boundary condition ⋮ Quasi-periodic solutions for a Schrödinger equation with a quintic nonlinear term depending on the time and space variables ⋮ Invariant tori of full dimension for higher-dimensional beam equations with almost-periodic forcing ⋮ Aspects of PDEs Related to Fluid Flows ⋮ Growth of Sobolev norms in 1-d quantum harmonic oscillator with polynomial time quasi-periodic perturbation ⋮ Reducibility and quasi-periodic solutions for a two dimensional beam equation with quasi-periodic in time potential ⋮ Quasi-periodic solutions for a Schrödinger equation under periodic boundary conditions with given potential ⋮ Quasi-periodic solutions for perturbed generalized KdV equation ⋮ Invariant Cantor manifolds of quasi-periodic solutions for the derivative nonlinear Schrödinger equation ⋮ A KAM theorem for higher dimensional nonlinear Schrödinger equations ⋮ Stability of KAM tori for nonlinear Schrödinger equation ⋮ A KAM theorem with applications to partial differential equations of higher dimensions ⋮ Exponential times in the one-dimensional Gross-Pitaevskii equation with multiple well potential ⋮ Periodic solutions for a class of nonlinear partial differential equations in higher dimension ⋮ KAM theory: The legacy of Kolmogorov's 1954 paper ⋮ Quasi-periodic solutions of fractional nonlinear Schrödinger equation systems ⋮ On the quasi-periodic solutions for generalized Boussinesq equation with higher order nonlinearity ⋮ Almost periodic solutions in forced harmonic oscillators with infinite frequencies ⋮ Unnamed Item ⋮ Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems ⋮ Quasi-periodic relativistic strings in the Minkowski space \(\mathbb{R}^{1+n}\) ⋮ On quantum averaging, quantum KAM, and quantum diffusion ⋮ KAM theory for the reversible perturbations of 2D linear beam equations ⋮ Almost-periodic solutions of an almost-periodically forced wave equation ⋮ Invariant tori for 1D quintic nonlinear wave equation ⋮ A Nekhoroshev type theorem for the nonlinear wave equation ⋮ Reducibility for Schrödinger operator with finite smooth and time-quasi-periodic potential ⋮ On reducibility of quantum harmonic oscillator on \(\mathbb{R}^d\) with quasiperiodic in time potential ⋮ Reducibility of 1D quantum harmonic oscillator perturbed by a quasiperiodic potential with logarithmic decay ⋮ Quasi-periodic solutions for a class of higher dimensional beam equation with quasi-periodic forcing ⋮ Reducibility of 1D quantum harmonic oscillator with decaying conditions on the derivative of perturbation potentials ⋮ Reducibility of quantum harmonic oscillator on $\mathbb{R}^d$ with differential and quasi-periodic in time potential ⋮ Reducibility of non-resonant transport equation on \({\mathbb {T}}^d\) with unbounded perturbations ⋮ Reducibility for wave equations of finitely smooth potential with periodic boundary conditions ⋮ Existence and Asymptotic Stability of Quasi-Periodic Solutions of Discrete NLS with Potential ⋮ A degenerate KAM theorem for partial differential equations with periodic boundary conditions ⋮ Quasi-periodic solutions of wave equations with the nonlinear term depending on the time and space variables ⋮ Quasi-periodic solutions for nonlinear Schrödinger equations with Legendre potential ⋮ Response solutions for quasi-periodically forced harmonic oscillators ⋮ On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range ⋮ Reducibility of 1-d quantum harmonic oscillator equation with unbounded oscillation perturbations ⋮ Kolmogorov-Arnold-Moser theorem for nonlinear beam equations with almost-periodic forcing ⋮ KAM for the derivative nonlinear Schrödinger equation with periodic boundary conditions ⋮ Melnikov's conditions in matrices ⋮ KAM theorem for a Hamiltonian system with sublinear growth frequencies at infinity ⋮ Invariant tori for two-dimensional nonlinear Schrödinger equations with large forcing terms ⋮ On quasi-periodic solutions for a generalized Boussinesq equation ⋮ Reducibility of Schrödinger equation at high frequencies ⋮ Reducible KAM tori for higher dimensional wave equations under nonlocal and forced perturbation ⋮ 1-d quantum harmonic oscillator with time quasi-periodic quadratic perturbation: reducibility and growth of Sobolev norms ⋮ Localization in one-dimensional quasi-periodic nonlinear systems ⋮ KAM tori for completely resonant Hamiltonian derivative beam equations on \(\mathbb{T}^2\) ⋮ Reducibility of Schrödinger equation on a Zoll manifold with unbounded potential ⋮ Quasi-periodic solutions of Schrodinger equations with quasi-periodic forcing in higher dimensional spaces ⋮ KAM Theorem for the Nonlinear Schrödinger Equation ⋮ Unnamed Item ⋮ A KAM theorem for reversible systems of infinite dimension ⋮ Reducibility of 1-d Schrödinger equation with unbounded time quasiperiodic perturbations. III ⋮ Large dispersion, averaging and attractors: three 1D paradigms ⋮ Lower dimensional invariant tori with prescribed frequency for the nonlinear Schrödinger equation ⋮ Long-Time Existence for Semi-Linear Klein–Gordon Equations with Quadratic Potential ⋮ Scattering for nonlinear Schrödinger equation under partial harmonic confinement ⋮ Quasiperiodic motions in dynamical systems: Review of a renormalization group approach ⋮ Long time stability of KAM tori for nonlinear wave equation ⋮ Quasi-periodic solutions for 1D wave equation with the nonlinearity \(u2p+1\) ⋮ On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity ⋮ Conserved quantities of some Hamiltonian wave equations after full discretization ⋮ Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds ⋮ Persistence of lower-dimensional hyperbolic invariant tori for generalized Hamiltonian systems ⋮ Degenerate lower-dimensional tori in Hamiltonian systems ⋮ Quasi-periodic solutions for a class of beam equation system ⋮ A KAM theorem for some partial differential equations in one dimension ⋮ Periodic and quasi-periodic solutions of a derivative nonlinear Schrödinger equation ⋮ ON THE EXISTENCE OF FULL DIMENSIONAL KAM TORUS FOR FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION ⋮ Periodic and quasi-periodic solutions for reversible unbounded perturbations of linear Schrödinger equations ⋮ Persistence of Lagrange invariant tori at tangent degeneracy ⋮ Unnamed Item ⋮ LONG TIME BEHAVIOR OF THE SOLUTIONS OF NLW ON THE -DIMENSIONAL TORUS ⋮ Almost periodic solutions for a class of linear Schrödinger equations with almost periodic forcing ⋮ Full dimension tori of Schrödinger equation ⋮ Construction of quasi-periodic solutions for the quintic Schrödinger equation on the two-dimensional torus $\mathbb {T}^2$ ⋮ Invariant tori for a derivative nonlinear Schrödinger equation with quasi-periodic forcing ⋮ Quasi-periodic solutions for d-dimensional beam equation with derivative nonlinear perturbation ⋮ Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres ⋮ The role of boundary conditions in the torsional instability of suspension bridges ⋮ Quasi-Periodic Solutions of Nonlinear Wave Equation with x-Dependent Coefficients ⋮ Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies ⋮ The existence of full-dimensional invariant tori for an almost-periodically forced nonlinear beam equation ⋮ Degenerate elliptic resonances ⋮ KAM tori for generalized Benjamin-Ono equation ⋮ KAM tori for a two dimensional beam equation with a quintic nonlinear term and quasi-periodic forcing ⋮ Stability of large periodic solutions of Klein-Gordon near a homoclinic orbit ⋮ Quasi-periodic solutions for nonlinear wave equation with singular Legendre potential ⋮ KAM tori for the two-dimensional completely resonant Schrödinger equation with the general nonlinearity ⋮ Reducible KAM tori for two-dimensional nonlinear Schrödinger equations with explicit dependence on the spatial variable ⋮ Quasiperiodic solutions of NLS with Liouvillean frequencies
