I am wondering what chaotic systems are from the perspective of numerical analysis. I am talking about 'deterministic chaos' such as for instance the 'logistic map' exhibits it. That is, the solution after many steps in the iterative solution is highly dependent on the initial conditions. It is clear that it will also be highly sensitive to numerical errors. But are chaotic systems

  • well posed (Hadamard),
  • well conditioned,
  • always unstable in implementations,
  • susceptible to regularization?
  • 1
    $\begingroup$ For numerical stability one might expect them to be backward-stable but not forward-stable - the sensitivity to initial conditions might enable you to find an exact initial condition whose evolution matches the numerical results. I believe these are called shadow solutions. $\endgroup$ – Kirill Sep 25 '15 at 20:34

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