Currently, the fifteen new periodic orbits of Newtonian three-body problem with equal mass were found by Šuvakov and Dmitra šinović [Phys Rev Lett, 2013, 110: 114301] using the gradient descent method with double precision. In this paper, these reported orbits are checked stringently by means of a reliable numerical approach (namely the “Clean Numerical Simulation”, CNS), which is based on the arbitrary-order Taylor series method and data in arbitrary-digit precision with a procedure of solution verification. It is found that seven among these fifteen orbits greatly depart from the periodic ones within a long enough interval of time, and are thus most possibly unstable at least. It is suggested to carefully check whether or not these seven unstable orbits are the so-called “computational periodicity” mentioned by Lorenz in 2006. This work also illustrates the validity and great potential of the CNS for chaotic dynamic systems.
three body problem periodic orbit stability computational reliability Clean Numerical Simulation (CNS)
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