Quadratic first integrals of autonomous conservative dynamical systems
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Publication:5140969
DOI10.1063/1.5141392zbMath1477.70034arXiv2007.11944OpenAlexW3098589366MaRDI QIDQ5140969
Michael Tsamparlis, Antonios Mitsopoulos
Publication date: 17 December 2020
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2007.11944
Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06)
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Cites Work
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- Lie point symmetries of a general class of PDEs: the heat equation
- Hidden symmetries and Killing tensors
- Generalizing the autonomous Kepler–Ermakov system in a Riemannian space
- Two-dimensional dynamical systems which admit Lie and Noether symmetries
- Polynomial constants of motion in flat space
- Geometrical classification of Killing tensors on bidimensional flat manifolds
- Killing tensors and symmetries
- Characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems. I. Velocity-dependent mappings of second-order differential equations
- Killing tensors in spaces of constant curvature
- Killing Tensors and Variable Separation for Hamilton-Jacobi and Helmholtz Equations
- Higher-order Noether symmetries and constants of the motion
- Generalizations of Noether’s Theorem in Classical Mechanics
- Dynamical Noether symmetries
- Invariant variation problems
- Symmetry groups and conserved quantities for the harmonic oscillator
- Killing tensors and conformal Killing tensors from conformal Killing vectors
- Darboux's problem of quadratic integrals
