Let's assume we have a multistable dynamical system
$\dot{x}=F(x)$
Furhter assume it has at least two (chaotic) attractors $A_1,A_2$ with basins of attraction $B(A_1),B(A_2)$.
How much information about the attractor $A_2$ is stored in the basin of attraction of attractor $B(A_1)$ and the attractor $A_1$ itself.
To specify what I mean by 'information'. Assuming there exist a perfect algorithm wich can find the ODE describing the attractor 1 $A_1$. If I now start the ODE with an initial condition in $B(A_2)$, will the system evolve into $A_2$ and how well will it describe $A_2$?
Possible example of two chaotic attractors:
