Note on integrability of certain homogeneous Hamiltonian systems

Abstract

In this paper we investigate a class of natural Hamiltonian systems with two degrees of freedom. The kinetic energy depends on coordinates but the system is homogeneous. Thanks to this property it admits, in a general case, a particular solution. Using this solution we derive necessary conditions for the integrability of such systems investigating differential Galois group of variational equations.

References in corpus (1)

• A note on algebraic potentials and Morales-Ramis theory

Cited by in corpus (9)

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• Integrability of certain Hamiltonian systems in $2D$ variable curvature spaces
• Superintegrability of 3-dimensional Hamiltonian systems with conformally Euclidean metrics. Oscillator-related and Kepler-related systems
• Integrability of non-homogeneous Hamiltonian systems with gyroscopic coupling
• Superintegrability on the 3-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the Sphere $S^3$ and on the Hyperbolic space $H^3$