Differential Galois obstructions for integrability of homogeneous Newton equations

DOI10.1063/1.2836412zbMath1153.81420arXivnlin/0701058OpenAlexW2044629502MaRDI QIDQ3544618

Maria Przybylska

Publication date: 8 December 2008

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0701058

Mathematics Subject Classification ID

Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Related Items (7)

Non-integrability of the semiclassical Jaynes-Cummings models without the rotating-wave approximation ⋮ Integrability analysis of chaotic and hyperchaotic finance systems ⋮ Integrability analysis of the stretch-twist-fold flow ⋮ Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application ⋮ Morales-Ramis theorems via Malgrange pseudogroup ⋮ The hydrogen atom in the van der Waals potential combined by magnetic and electric fields, Painlevé analysis, and integrability ⋮ Double tangent extension method and first integrals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Finiteness of integrable \(n\)-dimensional homogeneous polynomial potentials
• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
• Galois groups of second and third order linear differential equations
• Galoisian obstructions to integrability of Hamiltonian systems. I.
• Non-integrability of ABC flow
• Two generator subgroups of \(\text{SL}(2,\mathbf C)\) and the hypergeometric, Riemann, and Lamé equations
• All meromorphically integrable 2D Hamiltonian systems with homogeneous potential of degree 3
• A fixed-point theorem for endomorphisms of the projective space with applications to algebraic foliations
• Geometry and integrability of Euler-Poincaré-Suslov equations
• Darboux points and integrability of Hamiltonian systems with homogeneous polynomial potential
• On the absence of a real-analytic first integral for ABC flow when A=B
• Nonintegrability of the Suslov problem
• Algebraic Groups and Algebraic Dependence
• Differential Galois theory and non-integrability of Hamiltonian systems
• Around Jouanolou non-integrability theorem

This page was built for publication: Differential Galois obstructions for integrability of homogeneous Newton equations