Galoisian obstruction to the integrability of general dynamical systems

DOI10.1016/j.jde.2012.01.004zbMath1246.32017OpenAlexW2043767383MaRDI QIDQ414822

Shaoyun Shi, Wenlei Li

Publication date: 11 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.jde.2012.01.004

zbMATH Keywords

dynamical systemdifferential Galois theoryMorales-Ramis theorydifference Galois theory

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Meromorphic mappings in several complex variables (32H04) Ordinary differential equations on complex manifolds (34M45) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15) Linear ordinary differential equations and systems in the complex domain (34M03)

Related Items (12)

On integrability of the segmented disc dynamo: the effect of mechanical friction ⋮ On first integrals of a family of generalized Lorenz-like systems ⋮ PILOT-WAVE HYDRODYNAMICS: QUANTISATION OF PARTIAL INTEGRABILITY FROM A NONLINEAR INTEGRO-DIFFERENTIAL EQUATION OF THE SECOND ORDER ⋮ Complex dynamics of some Hamiltonian systems: nonintegrability of equations of motion ⋮ Kovalevskaya exponents, weak Painlevé property and integrability for quasi-homogeneous differential systems ⋮ Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application ⋮ Weak-Painlevé property and integrability of general dynamical systems ⋮ Darboux integrability of the stretch-twist-fold flow ⋮ Differential Galois integrability obstructions for nonlinear three-dimensional differential systems ⋮ Meromorphic and formal first integrals for the Lorenz system ⋮ Integrable deformations, bi-Hamiltonian structures and nonintegrability of a generalized Rikitake system ⋮ First integrals of the Maxwell-Bloch system

Cites Work

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• Non-integrability of Hénon-Heiles system
• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Galoisian obstructions to non-Hamiltonian integrability
• Non-integrability of some Hamiltonians with rational potentials
• Non-integrability of Hénon-Heiles system and a theorem of Ziglin
• An algorithm for solving second order linear homogeneous differential equations
• A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
• An algorithm determining the difference Galois group of second order linear difference equations
• Solving difference equations in finite terms
• Picard-Vessiot theory and Ziglin's theorem
• Galois theory of difference equations
• Non-integrability of the problem of a rigid satellite in gravitational and magnetic fields
• Non-integrability of ABC flow
• Nonintegrability of the Suslov problem
• Investigating non-integrability and chaos in complex time
• On non-integrability of general systems of differential equations
• Non-integrability criteria for Hamiltonians in the case of Lamé normal variational equations
• Differential Galois approach to the non-integrability of the heavy top problem
• Dynamics of Rational Symplectic Mappings and Difference Galois Theory
• A word of caution concerning the Yoshida criterion on algebraic integrability and Kowalevski exponents
• Group-theoretic obstructions to integrability
• Galoisian obstructions to integrability and Melnikov criteria for chaos in two-degree-of-freedom Hamiltonian systems with saddle centres
• Algebraic proof of the non-integrability of Hill's problem
• Necessary condition for the existence of algebraic first integrals
• Differential Galois theory and non-integrability of Hamiltonian systems

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