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In this paper, we present an application of the Shannon entropy in the caseof the planar (non-restricted) four-body problem. Specifically, the Kepler-60extrasolar system is being investigated with a primary interest in the resonantconfiguration of the planets that exhibit a chain of mean-motioncommensurabilities with the ratios 5:4:3. In the dynamical maps provided, theShannon entropy is utilized to explore the general structure of the phasespace, while, based on the time evolution of the entropy, we determine also theextent and rate of the chaotic diffusion as well as the characteristic times ofstability for the planets. Two cases are considered: (i) the pure Laplaceresonance when the critical angles of the 2-body resonances circulate and thatof the 3-body resonance librates; and (ii) the chain of two 2-body resonanceswhen all the critical angles librate. Our results suggest that case (ii) is themore favourable configuration but we state too that, in either case, therelevant resonance plays an important role to stabilize the system. The derivedstability times are no shorter than $10^8$ yrs in the central parts of theresonances.

Application of the Shannon entropy in the planar (non-restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system