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We consider the Kolmogorov problem of viscous incompressible planar fluid flow under external spatially periodic forcing. Looking for time-independent bounded solutions near the critical Reynolds number, we use the Kirchgaessner reduction to obtain a spatial dynamical system on a 6-dimensional center manifold. The dynamics is generated by translations in the unbounded spatial direction. Reduction by first integrals yields a 3-dimensional reversible system with a line of equilibria. This line of equilibria is neither induced by symmetries, nor by first integrals. At isolated points, normal hyperbolicity of the line fails due to a transverse double eigenvalue zero. We investigate such a "Bogdanov-Takens bifurcation without parameters'' by blow-up and averaging techniques. In particular we describe the set of all small bounded solutions. In the classical Kolmogorov case, this includes periodic profiles, homoclinic pulses and a heteroclinic front-back pair. This is a consequence of the double symmetry of the external force. In the more general case where only one symmetry is preserved,the set of bounded solutions consist entirely of trivial equilibria and multipulse heteroclinic pairs. The latter form  a very complicated, albeit non-recurrent, set. This is joint work with A. Afendikov and B. Fiedler.