  The leading Lie generators, including the chromatic effects, due to hard-edge
fringe field of single multipole and solenoid are derived from the vector
potentials within a Hamiltonian system. These nonlinear generators are applied
to the interaction region of PEP-II to analyze the linear errors due to the
feed-down from the off-centered quadrupoles and solenoid. The nonlinear effects
of tune shifts at large amplitude, the synchro-betatron sidebands near half
integer and their impacts on the dynamic aperture are studied in the paper.
