Shadowing Theorem

Although a numerically computed chaotic trajectory diverges exponentially from the true trajectory with the same initial coordinates, there exists an errorless trajectory with a slightly different initial condition that stays near ("shadows") the numerically computed one. Therefore, the fractal structure of chaotic trajectories seen in computer maps is real.

REFERENCES:

Ott, E. Chaos in Dynamical Systems. New York: Cambridge University Press, pp. 18-19, 1993.