Amplitude analysis of the decayB±→π±π±π∓

We present a Dalitz-plot analysis of charmless B+- decays to the final state pi+- pi+- pi-+ using 210 fb^-1 of data recorded by the BABAR experiment at sqrt(s) = 10.58 GeV. We measure the branching fractions B(B+- -> pi+- pi+- pi-+) = (16.2 +- 1.2 +- 0.9) x 10^-6 and B(B+- -> rho^0(770) pi+-) = (8.8 +- 1.0 +- 0.6 +0.1-0.7) x 10^-6. Measurements of branching fractions for the quasi-two-body decays B+- -> rho^0(1450) pi+-, B+- -> f_0(980) pi+- and B+- -> f_2(1270) pi+- are also presented. We observe no charge asymmetries for the above modes, and there is no evidence for the decays B+- -> chic0 pi+-, B+- -> f_0(1370) pi+- and B+- -> sigma pi+-.