A criterion of integrability for perturbed nonresonant harmonic oscillators. Wick Ordering of the perturbations in classical mechanics and invariance of the frequency spectrum

DOI10.1007/BF01206029zbMath0544.70026MaRDI QIDQ797009

Giovanni Gallavotti

Publication date: 1982

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

renormalizationWick orderinggeneric nonexistence of analytic integralsinvariance of the frequency spectrumn degree of freedomperturbations of integrable Hamiltonian systemstheorem of Poincaré

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (16)

High-order control for symplectic maps ⋮ On convergence of normal forms for complex frequencies ⋮ Resummation of perturbation series and reducibility for Bryuno skew-product flows ⋮ Convergence of a quantum normal form and an exact quantization formula ⋮ Spectral stability and semiclassical measures for renormalized KAM systems ⋮ Absolutely continuous spectra of quasiperiodic Schrödinger operators ⋮ Convergence of KAM iterations for counterterm problems ⋮ A uniform quantum version of the Cherry theorem ⋮ Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat ⋮ From dynamical systems to renormalization ⋮ Control of chaos in Hamiltonian systems ⋮ Quantum singular complete integrability ⋮ Quasiperiodic Hamiltonian motions, scale invariance, harmonic oscillators ⋮ Differential systems with Fuchsian linear part: correction and linearization, normal forms and multiple orthogonal polynomials ⋮ Convergence of the Birkhoff normal form sometimes implies convergence of a normalizing transformation ⋮ Around the stability of KAM tori

Cites Work

• Unnamed Item
• Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties
• The spectral class of the quantum-mechanical harmonic oscillator
• Critical Behavior of a KAM surface. I: Empirical results

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