Limitations of delay reconstruction for chaotic dynamical systems

We consider the problems arising in the application of algorithms of fractal-dimension measurements to data obtained from numerical integration of equations describing Rayleigh-Bénard convection. It is shown that in some cases the delay reconstruction of an attractor from a scalar time series requires much more data than does processing in the original phase space. If the length of the time series is too small, then the result resembles that for the case of large noise. © 1993 The American Physical Society.