  Aim. The eccentric von Zeipel-Lidov-Kozai (ZLK) effect is widely used to
explain dynamical phenomena in varieties of astrophysical systems. The purpose
of this work is to make clear the dynamical essence of the eccentric ZLK effect
by constructing an inherent connection between such an effect and dynamics of
secular resonance in restricted hierarchical planetary systems. Methods.
Dynamical structures of apsidal resonance are analytically studied by means of
perturbative treatments. The resonant model is formulated by averaging the
Hamiltonian (up to octupole order) over rotating ZLK cycles, producing an
additional motion integral. The phase portraits under the resonant model can be
used to analyse dynamical structures, including resonant centres, dynamical
separatrices and islands of libration. Results. By analysing phase portraits,
five branches of libration centres and eight libration zones are found in the
eccentricity--inclination space. There is an excellent agreement between
analytical results of libration zone and numerical distributions of resonant
orbit, indicating that the resonant model for apsidal resonances is valid and
applicable. Additionally, it is found that, in the test-particle limit,
distributions of flipping orbits are dominated by those apsidal resonances
centred at the inclination of i = 90 deg. Conclusions. The eccentric ZLK effect
is dynamically equivalent to the effect of apsidal resonance in restricted
hierarchical planetary systems. The dynamical response of the eccentric ZLK
effect (or effect of apsidal resonance) is to significantly excite
eccentricities and/or inclinations of test particles in the very long-term
evolution.
