First integrals and symmetries of time-dependent Hamiltonian systems

DOI10.1063/1.530206zbMath0781.70013OpenAlexW1999135135MaRDI QIDQ4201766

S. Bouquet, A. Dewisme

Publication date: 6 September 1993

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

Full work available at URL: https://doi.org/10.1063/1.530206

zbMATH Keywords

harmonic oscillatorLie symmetriesautonomous Hamiltonian

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

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Cites Work

• Lie symmetries of the Lorenz model
• Invariants for time-dependent potentials: Use of self-similar techniques
• Rational functions of momentum as invariants for one-dimensional, time-dependent potentials: Basic theory
• Nonlinear time-dependent anharmonic oscillator: Asymptotic behavior and connected invariants
• Invariants for dissipative nonlinear systems by using rescaling
• Lie group symmetries and invariants of the Hénon–Heiles equations
• Invariants of particle motion in one-dimensional time-dependent potentials
• Integrable Hamiltonians with higher transcendental invariants
• First integrals for some nonlinear time-dependent Hamiltonian systems
• Generalizations of Noether’s Theorem in Classical Mechanics
• Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes
• Representations of one-dimensional Hamiltonians in terms of their invariants
• Invariant variation problems
• Class of Exact Invariants for Classical and Quantum Time-Dependent Harmonic Oscillators