  Recent studies suggest that unstable recurrent solutions of the Navier-Stokes
equation provide new insights into dynamics of turbulent flows. In this study,
we compute an extensive network of dynamical connections between such solutions
in a weakly turbulent quasi-two-dimensional Kolmogorov flow that lies in the
inversion-symmetric subspace. In particular, we find numerous isolated
heteroclinic connections between different types of solutions -- equilibria,
periodic, and quasi-periodic orbits -- as well as continua of connections
forming higher-dimensional connecting manifolds. We also compute a homoclinic
connection of a periodic orbit and provide strong evidence that the associated
homoclinic tangle forms the chaotic repeller that underpins transient
turbulence in the symmetric subspace.
