Pretty interesting topic, would be interesting if it could be used to move satellites to a “parking orbit” once they run out of fuel. It’s unclear just how much movement in an orbit that can be done, as it says it needs to be in the same energy level.
Source press release: https://www.surrey.ac.uk/news/new-technique-uses-knot-theory-create-tube-map-around-planets-and-moons
Source journal article: https://link.springer.com/article/10.1007/s42064-024-0201-0
Seems to only work with N body type situations, meaning you wouldn’t likely see any possibilities in LEO or even GEO. This is more for systems like Jupiter or Saturn where you have lots of moons you can play with.
Right, I was responding to OPs comment with the article about putting satellites into final parking orbits when they run out of fuel.