  Asteroids in mean motion resonances with giant planets are common in the
solar system, but it was not until recently that several asteroids in
retrograde mean motion resonances with Jupiter and Saturn were discovered. A
retrograde co-orbital asteroid of Jupiter, 2015 BZ509 is confirmed to be in a
long-term stable retrograde 1:1 mean motion resonance with Jupiter, which gives
rise to our interests in its unique resonant dynamics. In this paper, we
investigate the phase-space structure of the retrograde 1:1 resonance in detail
within the framework of the circular restricted three-body problem. We
construct a simple integrable approximation for the planar retrograde resonance
using canonical contact transformation and numerically employ the averaging
procedure in closed form. The phase portrait of the retrograde 1:1 resonance is
depicted with the level curves of the averaged Hamiltonian. We thoroughly
analyze all possible librations in the co-orbital region and uncover a new
apocentric libration for the retrograde 1:1 resonance inside the planet's
orbit. We also observe the significant jumps in orbital elements for outer and
inner apocentric librations, which are caused by close encounters with the
perturber.
