Continuous homomorphisms on piecewise absolutely continuous maps of S1

Let IET(S1) be the group of interval exchange transformation of S1 and AC+(S1) be the group of absolutely continuous preserving orientation bijection with inverse absolutely continuous. We denote by PAC+(S1) the group generated by IET(S1) and AC+(S1). Given a suitable distance on PAC+(S1), we classify all continuous homomorphisms ρ : R → PAC+(S1). More precisely, ρ is conjugated to a continuous homomorphism ˆρ: R → AC+( i(S1)i).