In the two example problems there may be long sequences of identical motion that will then significantly diverge. That is, if you observe the object from t_i till t_j (with i,j > 0 and j > i) then this observation is not sufficient to distinguish better trajectories T_1 and T_2.
Chaotic systems are deterministic but highly sensitive to initial conditions. IIRC Lorenz said something like The present determines the future but the approximate present doesn't approximate the future
I don't find an issue with the line. To me it reads that to determine a systems parameters at t_i, you need to run the simulation from t_0. Which while not always true is more than accurate enough and is a common statement made when chaos is being taught. The accuracy just depends on how chaotic the system is and how long you measure for
Chaotic systems are deterministic but highly sensitive to initial conditions. IIRC Lorenz said something like The present determines the future but the approximate present doesn't approximate the future
I don't find an issue with the line. To me it reads that to determine a systems parameters at t_i, you need to run the simulation from t_0. Which while not always true is more than accurate enough and is a common statement made when chaos is being taught. The accuracy just depends on how chaotic the system is and how long you measure for