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GeezerVison is showing mathworld.wolfram.com — Shadowing Theorem -- from Wolfram MathWorld 
Shadowing TheoremAlthough 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. Explore with Wolfram|Alpha
More things to try: ReferencesOtt, E. Chaos in Dynamical Systems. New York: Cambridge University Press, pp. 18-19, 1993.Referenced on Wolfram|AlphaShadowing TheoremCite this as:Weisstein, Eric W. "Shadowing Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ShadowingTheorem.html Subject classifications |
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