  Analytic expressions for the amplitude-dependent tune shift driven by the
quadrupole magnet fringe field have been obtained. The magnitude of the effect
is compared with other sources of non-linearity such as chromatic sextupoles,
octupole errors of the main quadrupole magnetic field and kinematic terms. A
numerical example was the calculation on the lattice of the VEPP-4M e+e-
collider.
