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We report on the long-term dynamical evolution of the two-planet Kepler-36system, which we studied through numerical integrations of initial conditionsthat are consistent with observations of the system. The orbits are chaoticwith a Lyapunov time of only ~10 years. The chaos is a consequence of aparticular set of orbital resonances, with the inner planet orbiting 34 timesfor every 29 orbits of the outer planet. The rapidity of the chaos is due tothe interaction of the 29:34 resonance with the nearby first order 6:7resonance, in contrast to the usual case in which secular terms in theHamiltonian play a dominant role. Only one contiguous region of phase space,accounting for ~4.5% of the sample of initial conditions studied, correspondsto planetary orbits that do not show large scale orbital instabilities on thetimescale of our integrations (~200 million years). The long-lived subset ofthe allowed initial conditions are those that satisfy the Hill stabilitycriterion by the largest margin. Any successful theory for the formation ofthis system will need to account for why its current state is so close tounstable regions of phase space.

Rapid dynamical chaos in an exoplanetary system