Two generator subgroups of \(\text{SL}(2,\mathbf C)\) and the hypergeometric, Riemann, and Lamé equations

DOI10.1006/jsco.1999.0313zbMath0958.34074OpenAlexW2004930414MaRDI QIDQ1974706

Richard C. Churchill

Publication date: 8 May 2000

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.1999.0313

zbMATH Keywords

explicit solutionsLamé equationdifferential Galois grouphypergeometric and Riemann equationsKovacic algorithmsecond-order linear homogeneous differential equations

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Applications of Lie groups to the sciences; explicit representations (22E70) Quantum groups (quantized function algebras) and their representations (20G42) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21) Ordinary differential equations on complex manifolds (34M45) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Related Items (10)

Semistable reduction of modular curves associated with maximal subgroups in prime level ⋮ Liouvillian solutions of Whittaker-Ince equation ⋮ On the absence of an additional meromorphic first integral in the Riemann problem on the motion of a homogeneous liquid ellipsoid ⋮ Integrability analysis of the stretch-twist-fold flow ⋮ Necessary conditions for super-integrability of Hamiltonian systems ⋮ Algebraic solutions of the Lamé equation, revisited. ⋮ Differential Galois obstructions for integrability of homogeneous Newton equations ⋮ An example of a modular foliation deducted from an algebraic solution of Painlevé VI equation ⋮ Jordan obstruction to the integrability of Hamiltonian systems with homogeneous potentials ⋮ MONODROMY ARISING FROM THE MARKOFF THEORY

Cites Work

• Note on Kovacic's algorithm
• Existence of exponentially unstable periodic solutions and the non- integrability of homogeneous Hamiltonian systems
• 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
• Monodromy for the hypergeometric function \(_ nF_{n-1}\)
• Non-integrability of the truncated Toda lattice Hamiltonian at any order
• On algebraic solutions of Lame's differential equation
• Kovacic's algorithm and its application to some families of special functions
• Picard-Vessiot theory and Ziglin's theorem
• Galois groups of second and third order linear differential equations
• Liouvillian and algebraic solutions of second and third order linear differential equations
• On a Galoisian approach to the splitting of separatrices
• Analytic non-integrability of the truncated two fixed centres problem in the symmetric case
• Non-integrability criteria for Hamiltonians in the case of Lamé normal variational equations
• Solution of the Inverse Problem of Differential Galois Theory in the Classical Case
• On Second Order Linear Differential Equations with Algebraic Solutions
• On the Determination of Ziglin Monodromy Groups
• Monodromy groups and Hill's equation
• On Monodromy Groups of Second-Order Fuchsian Equations
• Complexity in spatio-temporal dynamics
• Rigid Local Systems. (AM-139)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Two generator subgroups of \(\text{SL}(2,\mathbf C)\) and the hypergeometric, Riemann, and Lamé equations