  A resonant chain may be formed in a multi-planetary system when ratios of the
orbital periods can be expressed as ratios of small integers $T_1:T_2: \cdots
:T_N=k_1: k_2: \cdots: k_N$. We investigate the dynamics and possible formation
of resonant chain. The appropriate Hamiltonian for a three-planet resonant
chain is defined and numerically averaged over the synodic period. The stable
stationary solutions (apsidal corotational resonance, ACR) of this system,
corresponding to the local extrema of Hamiltonian function, can be searched out
numerically. The topology of the Hamiltonian around these ACRs reveals their
stabilities. We further construct dynamical maps on representative planes to
study the dynamics, and we calculate the deviation ($\chi^2$) of the resonant
angle from the uniformly distributed values. Finally, the formation of resonant
chain via convergent migration is simulated and stable configurations
associated with ACRs are verified. We find that stable ACR families arising
from circular orbits always exist for any resonant chain, and they may extend
to high eccentricity. Around ACR solutions, regular motion are found in two
types of resonant configurations. One is characterised by libration of both the
two-body resonant angles and the three-body Laplace resonant angle, and the
other by libration of only two-body resonant angles. The Laplace resonance
seems not to contribute much to the stability. The resonant chain can be formed
via convergent migration, and subsequently the resonant configuration evolves
along the ACR families to eccentric orbits. Ideally, our methods introduced
here can be applied to any resonant chain of any number of planets at any
eccentricity.
