One-dimensional nonautonomous dynamical systems with exact transcendental invariants

DOI10.1063/1.529589zbMath0761.58060OpenAlexW2090692976MaRDI QIDQ4032259

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Publication date: 1 April 1993

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

Full work available at URL: https://doi.org/10.1063/1.529589

zbMATH Keywords

dynamical systemsparticle motionVlasov-Poisson equationsBBGKY equation

Mathematics Subject Classification ID

Applications of global analysis to the sciences (58Z05) Applications of dynamical systems (37N99) Classical field theories (70Sxx)

Related Items (5)

Search for first integrals in relativistic time-dependent Hamiltonian systems ⋮ Completely integrable one-dimensional classical and relativistic time-dependent Hamiltonians ⋮ Hamiltonian structure and integrability of the stationary Kuramoto–Sivashinsky equation ⋮ Extension of Giacomini’s results concerning invariants for one-dimensional time-dependent potentials ⋮ A stability criterion for a class of discrete nonlinear systems with random parameters

Cites Work

• A resonance formulation for invariants of particle motion in a one- dimensional time-dependent potential
• Rational functions of momentum as invariants for one-dimensional, time-dependent potentials: Basic theory
• Polynomial constants of motion in flat space
• Invariants for dissipative nonlinear systems by using rescaling
• Integrable Hamiltonians with higher transcendental invariants
• A direct approach to finding exact invariants for one-dimensional time-dependent classical Hamiltonians
• Exact time-dependent solutions of the Vlasov–Poisson equations
• Integrable potentials with logarithmic integrals of motion
• Construction of new integrable Hamiltonians in two degrees of freedom

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