Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem.

  title={Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem.},
  author={Lyudmila Grigoryeva and Allen G. Hart and Juan-Pablo Ortega},
  journal={Physical review. E},
  volume={103 6-1},
This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result provides a powerful tool for the representation, reconstruction, and forecasting of chaotic attractors. It also improves previous statements in the literature for differentiable generalized synchronizations, whose existence was so far guaranteed for a… 

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