The accepted MNRAS paper here, Fig 1b (and described in Sec. 4), shows the semi-major axis alternates between about 1.004 and 0.996  AU, with a period of about 350 years.  Fig 1a shows the horseshoe shape, as seen in the rotating coordinate system. (Note however that according to the caption for Fig 1a only, "The radial extent of the horseshoe oscillations has been exaggerated by a factor of 20 for clarity".)  This libration pattern is stable for over 200,000 yr, which is >500 repetitions of the horseshoe.