Critical points of the systole function

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(CIRM 2022) Using the Delaunay tesselation it should be possible to locate the critical point of the systole functions inside Teichmüller discs. By systole, we mean the shortest curve in a given family. The ones of interest are

• saddle connections
• saddle connections of a given type (ie with specified start and end in the surface and, if start=end, a specified angle)
• closed curve
• separating closed curve