  We study the dynamical chaos and integrable motion in the planar circular
restricted three-body problem and determine the fractal dimension of the spiral
strange repeller set of non-escaping orbits at different values of mass ratio
of binary bodies and of Jacobi integral of motion. We find that the spiral
fractal structure of the Poincar\'e section leads to a spiral density
distribution of particles remaining in the system. We also show that the
initial exponential drop of survival probability with time is followed by the
algebraic decay related to the universal algebraic statistics of Poincar\'e
recurrences in generic symplectic maps.
