On the summation of the Birkhoff–Gustavson normal form of an anharmonic oscillator
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Publication:4723332
DOI10.1063/1.527048zbMath0615.70012OpenAlexW2037168185MaRDI QIDQ4723332
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Publication date: 1986
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.527048
Padé approximantsanharmonic oscillatorBirkhoff-Gustavson normal formradius of convergenceglobal nonintegrabilitytorus quantization
Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)
Related Items (5)
Application of normal forms to the Lorenz model in the subcritical region ⋮ Program for Birkhoff-Gustavson normal form for \(N\) degrees of freedom -- BIRKHOFF 1.2 ⋮ Perturbation theory and the classical limit of quantum mechanics ⋮ Decoupling of dissipative flows by interval normal forms in the Poincaré domain ⋮ The Birkhoff–Gustavson normal form of one-dimensional double-well Hamiltonians
Cites Work
- Three integrable Hamiltonian systems connected with isospectral deformations
- Iterative solutions of nonlinear initial value differential equations in Chebyshev series using Lie series
- Determination of eigenvalues by divergent perturbation series
- On the integrals of canonical systems
- A simple eigenvalue formula for the quartic anharmonic oscillator
- The eigenvalues of the bounded λx2moscillators
- Exact solutions of the Schrödinger equation for a class of three-dimensional isotropic anharmonic oscillators
- Extended continued fractions and energies of the anharmonic oscillators
- On the Laplace asymptotic expansion of conditional Wiener integrals and the Bender–Wu formula for x2N-anharmonic oscillators
- Anharmonic oscillators and generalized hypergeometric functions
- A summation method for the Rayleigh–Schrödinger series for the anharmonic oscillator
- Canonical transformations depending on a small parameter
- Perturbation method in the theory of nonlinear oscillations
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