Context : The Gaia ESO Public Spectroscopic Survey ( GES ) is providing the astronomical community with high-precision measurements of many stellar parameters including radial velocities ( RVs ) of stars belonging to several young clusters and star-forming regions .
One of the main goals of the young cluster observations is to study of their dynamical evolution and provide insight into their future , revealing if they will eventually disperse to populate the field , rather than evolve into bound open clusters .

Aims : In this paper we report the analysis of the dynamical state of L1688 in the \rho Ophiuchi molecular cloud using the dataset provided by the GES consortium .

Methods : We performed the membership selection of the more than 300 objects observed .
Using the presence of the lithium absorption and the location in the Hertzspung-Russell diagram , we identify 45 already known members and two new association members .
We provide accurate RVs for all 47 confirmed members .

Results : A dynamical analysis , after accounting for unresolved binaries and errors , shows that the stellar surface population of L1688 has a velocity dispersion \sigma \sim 1.14 \pm 0.35 km s ^ { -1 } that is consistent with being in virial equilibrium and is bound with a \sim 80 % probability .
We also find a velocity gradient in the stellar surface population of \sim 1.0 km s ^ { -1 } pc ^ { -1 } in the northwest/southeast direction , which is consistent with that found for the pre-stellar dense cores , and we discuss the possibility of sequential and triggered star formation in L1688 .

Conclusions :