  The double coplanar pendulum is an example of the coexistence of regular and
chaotic dynamics for equal energy values but different initial conditions.
Regular trajectories predominate for low energies; as the energy is increased,
the system passes through values where chaotic trajectories are abundant, and
then, increasing the energy further, it is again dominated by regular
trajectories. Given that the energetically accessible states are bounded, a
relevant question is about the fraction of phase space regular or chaotic
trajectories as the energy varies. In this paper, we calculate the relative
abundance of chaotic trajectories in phase space, characterizing the
trajectories using the maximum Lyapunov exponent, and find that, for low
energies, it grows exponentially.
