Optimal successive linearization method to calculate dynamic aperture

It is pointed out that successive linearization method, namely, the distribution of initial conditions is arbitrary and the second order correction needs to be taken into account. To keep the advantages of the method and to get a solution as faithful as possible, the differential equation at second step is optimally linearized. It reduces the arbitrariness in the distribution of initial conditions. Using this method calculation of distortion of invariant curves can also be done. (author). 5 refs