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 Poincare 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 Poincare recurrences in generic symplectic maps.
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