Higher order first integrals of autonomous dynamical systems

Abstract

A theorem is derived which determines higher order first integrals of autonomous holonomic dynamical systems in a general space, provided the collineations and the Killing tensors -- up to the order of the first integral -- of the kinetic metric, defined by the kinetic energy of the system, can be computed. The theorem is applied in the case of Newtonian autonomous conservative dynamical systems of two degrees of freedom, where known and new integrable and superintegrable potentials that admit cubic first integrals are determined.

References in corpus (11)

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Cited by in corpus (6)

• Classification of the Lie and Noether symmetries for the Klein-Gordon equation in Anisotropic Cosmology
• Hidden symmetries from distortions of the conformal structure
• Quadratic first integrals of constrained autonomous conservative dynamical systems with fixed energy
• Cubic first integrals of autonomous dynamical systems in $E^2$ by an algorithmic approach
• Higher order first integrals of autonomous non-Riemannian dynamical systems
• Higher order first integrals of autonomous dynamical systems in terms of geometric symmetries