# Commit 2020-12-07 10:37 44400c99

View on Github →feat(dynamics/circle/rotation_number): translation numbers define a group action up to a semiconjugacy (#5138)
Formalize a theorem by Étienne Ghys: given two lifts `f₁`

, `f₂`

of
actions of a group `G`

on the circle by orientation preserving
homeomorphisms to the real line, assume that for each `g : G`

the
translation numbers of `f₁ g`

and `f₂ g`

are equal. Then the actions
are semiconjugate by a (possibly discontinuous) circle map.