From the preceding discussion, it should be apparent that the decay rate, the fractal dimension and the Lyapunov exponents are all related.  The large Lyapunov exponent, for instance, tells us how fast a trajectory in the invariant set will diverge if perturbed.  Similarly, the fractal dimension will give us information about the density of orbits in the invariant set.  Thus we can see that both will affect the decay rate as captured in the following conjecture for a two-dimensional scattering system:
where D is the information dimension and h and h are the small and large Lyapunov exponents, respectively.  For an attractor,  and it reduces to the Kaplan–Yorke conjecture.