Timeline for Which surfaces admit unbounded-length simple geodesics?
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| Feb 24, 2023 at 23:38 | comment | added | Paolo Piccione | In this example, the sequence of arbitrary long simple geodesics turns around a stable closed geodesic (the thinner waist). Is it always the case that, if a surface admits arbitrarily long simple geodesics, then there must be a stable closed geodesic? | |
| May 14, 2017 at 0:48 | comment | added | Pengfei | I think the Anosov's picture is pretty similar to those described in Akopyan--Petrunin's paper (provided in the question). Beside the smoothness v.s. convexity, the main difference is that Anosov deformed the spherical cap to twist the direction, while Akopyan--Petrunin utilized the singularity to make the twist. | |
| May 11, 2017 at 21:51 | history | answered | Pengfei | CC BY-SA 3.0 |