On a class of variational equations transformable to the Gauss hypergeometric equation

DOI10.1007/BF00049462zbMath0756.34016OpenAlexW2083377024MaRDI QIDQ1192271

Haruo Yoshida

Publication date: 27 September 1992

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00049462

zbMATH Keywords

stabilityHamiltonian systemsvariational equationsmonodromy matricesregions of instabilityeigenvalues for HessianGauss hypergeometric equationgeneralized Hamiltonian setuplinear ordinary differential equations with periodic coefficients

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (2)

Non-integrability of first order resonances in Hamiltonian systems in three degrees of freedom ⋮ Meromorphic nonintegrability of Hamiltonian systems

Cites Work

• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• 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
• Non-integrability of the truncated Toda lattice Hamiltonian at any order
• A criterion for the nonexistence of an additional analytic integral in Hamiltonian systems with \(n\) degrees of freedom
• A type of second order linear ordinary differential equations with periodic coefficients for which the characteristic exponents have exact expressions
• Exponential instability of collision orbit in the anisotropic Kepler problem

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