Arbitrary order numerical solutions conserving the Jacobi constant in the motion near the equilibrium points

In the paper a modification of the polynomial extrapolation for solving the problem of motion nearby the equilibrium points is presented. It appears that the modification yields a better approximation of the exact solution than the convential polynomial extrapolation and other methods. Moreover, the modification conserves the Jacobi constant of motion. Computer examples for orbits nearby the equilibrium points of the Sun-Jupiter system are given.