Tidal evolution of a Jupiter-mass planet starting at different initial semi-major axis around either fast-rotating or a slow-rotating 0.1   M_⊙ star. Top panel: evolution of semi-major axis of a a planet around an initially fast rotating M-dwarf (bold solid lines) and around an initially slow rotating M-dwarf (dashed dotted lines). Bottom panel: rotation period of initially fast rotators (solid lines) and slow rotators (dashed dotted lines). The black long dashes represent T_sat = 2π/ω_sat. The red curves represent the evolution of the spin of the star if there is no planet.