  We study the capture of galactic dark matter particles in the Solar System
produced by rotation of Jupiter. It is shown that the capture cross section is
much larger than the area of Jupiter orbit being inversely diverging at small
particle energy. We show that the dynamics of captured particles is chaotic and
is well described by a simple symplectic dark map. This dark map description
allows to simulate the scattering and dynamics of $10^{14}$ dark matter
particles during the life time of the Solar System and to determine dark matter
density profile as a function of distance from the Sun. The mass of captured
dark matter in the radius of Neptune orbit is estimated to be $2 \cdot 10^{15}
g$. The radial density of captured dark matter is found to be approximately
constant behind Jupiter orbit being similar to the density profile found in
galaxies.
