<p>Classical attempts to construct a galaxy model, in a stationary and axisymmetric situation, consist of giving a gravitational field and injecting it into the collisionless Boltzmann equation to deduce the solution distribution function f. We will do exactly the opposite, by assimilating the galaxy to a self-gravitating point-mass system. The velocity distribution function is then the solution of an integrodifferential equation. Taking into account the Newtonian character of the potential, we can replace it with the system consisting of the Vlasov equation, written in terms of residual velocity, and the Poisson equation. We then give <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>l</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>f</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$ln(f)$</EquationSource> </InlineEquation> the form of a polynomial of degree 2, such that one of the axes of the velocity ellipsoid points towards the center of the system. This single constraint gives the evolution of the axes in space, these being equal to the center of the galaxy (Maxwell-Boltzmann distribution). Moving away from the center, the axis pointing in this direction remains constant while the transverse axes tend to zero at infinity. We then construct the macroscopic velocity field by excluding any vortex structure. This field then tends towards a solid body rotation at the center. The velocity tends towards a remote plateau, which is then consistent with the observational data.</p>