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arXiv · 2010.03218

Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem

Lyudmila Grigoryeva·Allen Hart·Juan-Pablo Ortega
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Abstract

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 restricted family of systems and was detected using H\"older exponent-based criteria.

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Lyudmila Grigoryeva, Allen Hart, Juan-Pablo Ortega. 2020-10-07. Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem. https://doi.org/10.1103/physreve.103.062204

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