conjugate points

The distance between these two conjugate points was equal to the length of a simple pendulum with the same period.

On , there are no conjugate points.

Especially with France she developed a program studying activity at geomagnetic conjugate points in the southern and northern hemispheres.

In differential geometry, conjugate points are, roughly, points that can almost be joined by a 1-parameter family of geodesics.

A Riemannian metric without conjugate points on n-dimensional torus is flat."

From the focusing theorem, we know that all geodesics from have conjugate points at finite values of the affine parameter.

The caustic determined by a given point "P" (in the image the point is at infinity) is the set of conjugate points to "P".

For example, Morse showed that the number of conjugate points in a trajectory equaled the number of negative eigenvalues in the second variation of the Lagrangian.

Conjugate points two points p and q on a geodesic are called conjugate if there is a Jacobi field on which has a zero at p and q.

More generally, volume entropy equals topological entropy under a weaker assumption that M is a closed Riemannian manifold without conjugate points (Freire and Mañé).

Suppose p and q are points on a Riemannian manifold, and is a geodesic that connects p and q. Then p and q are conjugate points along if there exists a non-zero Jacobi field along that vanishes at p and q.