SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems
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Publication:3778301
DOI10.1063/1.528139zbMath0637.34032OpenAlexW1978478309MaRDI QIDQ3778301
No author found.
Publication date: 1988
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.528139
Lie algebraexamplessimilarity analysisfinite symmetry transformationsinhomogeneous ordinary linear differential equation of the second order
Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Lie algebras of Lie groups (22E60)
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Contact symmetry algebras of scalar second-order ordinary differential equations, Symmetry Lie algebras of \(n\)th order ordinary differential equations, Heuristic approach to non-Abelian quantum kinematics and dynamics in configuration spacetime, SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems. III. Equivalent Lagrangian formalisms, Perturbation to conformal invariance and adiabatic invariants of generalized perturbed Hamiltonian system with additional terms, On the complete symmetry group of the classical Kepler system, Point symmetry group of the Lagrangian, Perturbation of symmetries of rotational relativistic Birkhoffian systems and its inverse problem, Lie symmetries, perturbation to symmetries and adiabatic invariants of Lagrange system, Characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems. IV. Classical (velocity-independent) mappings of second-order differential equations, Perturbation to Mei symmetry and generalized Mei adiabatic invariants for Birkhoffian systems, SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems. II. Realizations of the Lie algebra
Cites Work
- Non-Noether constants of motion
- A complete classification of dynamical symmetries in classical mechanics
- Quantum kinematics of the harmonic oscillator
- Infinitesimal symmetry transformations. II. Some one-dimensional nonlinear systems
- Some remarks on the Lie group of point transformations for the harmonic oscillator
- The complete symmetry group of the one-dimensional time-dependent harmonic oscillator
- On the Lie symmetries of the classical Kepler problem
- The Lie group of Newton's and Lagrange's equations for the harmonic oscillator
- Related integral theorem. II. A method for obtaining quadratic constants of the motion for conservative dynamical systems admitting symmetries
