Conjugate points for systems of second-order ordinary differential equations

Abstract

We recall the notion of Jacobi fields, as it was extended to systems of second-order ordinary differential equations. Two points along a base integral curve are conjugate if there exists a non-trivial Jacobi field along that curve that vanishes on both points. Based on arguments that involve the eigendistributions of the Jacobi endomorphism, we discuss conjugate points for a certain generalization (to the current setting) of locally symmetric spaces. Next, we study conjugate points along relative equilibria of Lagrangian systems with a symmetry Lie group. We end the paper with some examples and applications.

23 pages, 1 figure

References in corpus (2)

• Cut locus of a left invariant Riemannian metric on SO(3) in the axisymmetric case
• Relative equilibria of Lagrangian systems with symmetry

Cited by in corpus (1)

• Jacobi fields and conjugate points for a projective class of sprays