Dynamic aperture estimates and phase space distortions in nonlinear betatronic motion

Symplectic mappings which modelize the 4D betatronic motion in a magnetic lattice are considered. We define the dynamic aperture in terms of the connected volume in phase space of initial conditions which are bounded for a given number of iterations. Different methods for a fast estimate of this quantity are given; the analysis of the associated errors and the optimization of the integration steps are outlined. A comparison of the accuracy of these methods is given for both simple models and more realistic lattices.