Geometrical aspects of Ziglin's non-integrability theorem for complex Hamiltonian systems

DOI10.1016/0022-0396(88)90065-4zbMath0661.58013OpenAlexW1965136018MaRDI QIDQ1113147

Richard C. Churchill, David L. Rod

Publication date: 1988

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(88)90065-4

zbMATH Keywords

monodromy groupnon-integrabilitycomplex Hamiltonian systems

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (max. 100)

Nonintegrability of the classical Zeeman Hamiltonian ⋮ A criterion for non-integrability based on Poincaré's theorem ⋮ Nonintegrability of some Hamiltonian systems, scattering and analytic continuation ⋮ Non-perturbative non-integrability of non-homogeneous nonlinear lattices induced by non-resonance hypothesis ⋮ On the holonomy group associated with analytic continuations of solutions for integrable systems ⋮ Obstructions to integrability of nearly integrable dynamical systems near regular level sets ⋮ Monodromy and nonintegrability in complex Hamiltonian systems ⋮ Completion of vector fields and the Painlevé property ⋮ Persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems ⋮ A note on Kowalevski exponents and the non-existence of an additional analytic integral ⋮ Non integrability of the \(J_ 2\) problem ⋮ A non-integrability test for perturbed separable planar Hamiltonians ⋮ Non-integrable Hamiltonian systems and the Heun equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A criterion for non-integrability of Hamiltonian systems with nonhomogeneous potentials
• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• Non-integrability of Hénon-Heiles system and a theorem of Ziglin
• Existence of exponentially unstable periodic solutions and the non- integrability of homogeneous Hamiltonian systems
• A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
• On the non-integrability of some generalized Toda lattices
• Non-integrability of the truncated Toda lattice Hamiltonian at any order
• Pathology in dynamical systems. III: Analytic Hamiltonians
• Complex manifolds without potential theory. (With an appendix on the geometry of characteristic classes). 2nd ed
• Pathology in dynamical systems. II: Applications
• Monodromy groups and linearly polymorphic functions
• Addendum to ``Hyperbolic periodic orbits
• Equations différentielles à points singuliers réguliers
• Integrability and non-integrability in Hamiltonian mechanics
• A type of second order linear ordinary differential equations with periodic coefficients for which the characteristic exponents have exact expressions
• Homoclinic and heteroclinic orbits of reversible vectorfields under perturbation
• Exponential instability of collision orbit in the anisotropic Kepler problem
• Braids, hypergeometric functions, and lattices
• On Second Order Linear Differential Equations with Algebraic Solutions
• On Second Order Linear Differential Equations with Algebraic Solutions on Algebraic Curves
• Some remarks on parallelizable Stein manifolds
• Necessary condition for the existence of algebraic first integrals

This page was built for publication: Geometrical aspects of Ziglin's non-integrability theorem for complex Hamiltonian systems