Abstract
A new class of linear ordinary differential equations with periodic coefficients is found which can be transformed to the Gauss hypergeometric equation, and therefore the monodromy matrices are computable explicitly. These equations appear as the variational equations around a straight-line solution in Hamiltonian systems of the form H = T(p) + V(q), where T(p) and V(q) are homogeneous functions of p and q, respectively.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yoshida, H.: 1984, ‘A Type of Second Order Ordinary Differential Equations with Periodic Coefficients for which the Characteristic Exponents have Exact Expressions’, Celest. Mech. 32, 73–86.
Yoshida, H.: 1986, ‘Existence of Exponentially Unstable Periodic Solutions and the Non-Integrability of Homogeneous Hamiltonian Systems’, Physica D 21, 163–170.
Yoshida, H.: 1987a, ‘Exponential Instability of the Collision Orbits in the Anisotropic Kepler Problem’, Celest. Mech. 40, 51–66.
Yoshida, H.: 1987b, ‘A Criterion for the Non-Existence of an Additional Integral in Hamiltonian Systems with a Homogeneous Potential’, Physica D 29, 128–142.
Yoshida, H.: 1988, ‘Non-Integrability of the Truncated Toda Lattice at any Order’, Commun. Math. Phys. 116, 529–538.
Yoshida, H.: 1989, ‘A Criterion for the Non-Existence of an Additional Analytic Integral in Hamiltonian Systems with N-degrees of Freedom’, Phys. Lett. A 141, 108–112.
Ziglin, S.L.: 1983, ‘Branching of Solutions and the Nonexistence of First Integrals in Hamiltonian Mechanics’, Func. Anal. Appl. 16, 181–189.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yoshida, H. On a class of variational equations transformable to the Gauss hypergeometric equation. Celestial Mech Dyn Astr 53, 145–150 (1992). https://doi.org/10.1007/BF00049462
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00049462