Multipole compensation in the LHC low-$\beta$ insertions

The LHC dynamic aperture in Physics conditions is determined by the field errors in the low-b quadrupoles and these errors set a lower limit to the value of b*. The associated aberrations have been computed with the transfer matrix method which gives particularly simple and efficient formulae for the case of low-b insertions. These formulae have been applied to the LHC case to design a multipole compensation system. The efficiency of the method has been assessed by trajectory tracking.