Dimensionality and integrals of motion of the Trappist-1 planetary system

Abstract

The number of isolating integrals of motion of the Trappist-1 system - a late M-dwarf orbited by seven Earth-sized planets - was determined numerically, using an adapted version of the correlation dimension method. It was found that over the investigated time-scales of up to 20 000 years the number of isolating integrals of motion is the same as one would find for a system of seven non-interacting planets - despite the fact that the planets in the Trappist-1 system are strongly interacting. Considering perturbed versions of the Trappist-1 system shows that the system may occupy an atypical part of phase-space with high stability. These findings are consistent with earlier studies.