Conjugate points on manifolds are, roughly speaking, points which are connected by a multitude of geodesics, so that there are problems with uniqueness of the shortest path between the points.
In symplectic geometry there is the concept of caustics, https://en.wikipedia.org/wiki/Caustic_(mathematics). These seem to be related to concentration of rays. My knowledge of symplectic geometry is not formidable, and it would take a bunch of reading to get a handle of that definition, so a question:
**Is there a connection between caustics and conjugate points?**
I would appreciate an explanation that is more about intuitive understanding than a formal proof, though of course a more formal explanation is also very welcome.
tommi
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2023-02-20T11:16:07Z (almost 2 years ago)