A Reduction Method for Higher Order Variational Equations of Hamiltonian Systems

zbMath1243.37048arXiv1206.6345MaRDI QIDQ3100079

Ainhoa Aparicio Monforte, Jacques-Arthur Weil

Publication date: 22 November 2011

Full work available at URL: https://arxiv.org/abs/1206.6345

zbMATH Keywords

Hamiltonian systemsdifferential Galois theorydifferential fieldreduced formshigher-order variational equationsobstructions to integrability

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Explicit solutions, first integrals of ordinary differential equations (34A05) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Related Items (9)

A characterization of reduced forms of linear differential systems ⋮ Liouville integrability: an effective Morales-Ramis-Simó theorem ⋮ A reduced form for linear differential systems and its application to integrability of Hamiltonian systems ⋮ Linearised higher variational equations ⋮ Picard-Vessiot theory and integrability ⋮ Integrability of potentials of degree \(k \neq \pm 2\). Second order variational equations between Kolchin solvability and abelianity ⋮ Integrable planar homogeneous potentials of degree \(- 1\) with small eigenvalues ⋮ Differential Galois Theory and Integration ⋮ Computing the Lie algebra of the differential Galois group: the reducible case

This page was built for publication: A Reduction Method for Higher Order Variational Equations of Hamiltonian Systems