Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem

Lyudmila Grigoryeva, Allen Hart, Juan Pablo Ortega

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11 Citations (SciVal)


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 Hölder exponent-based criteria.

Original languageEnglish
Article number062204
JournalPhysical Review E
Issue number6
Publication statusPublished - 3 Jun 2021

Bibliographical note

Funding Information:
A.H. is supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), Project No. EP/L015684/1. J.-P.O. acknowledges partial financial support coming from the Research Commission of the Universität Sankt Gallen, the Swiss National Science Foundation (grant number 200021_175801/1), and the French ANR “BIPHOPROC” Project No. (ANR-14-OHRI-0002-02). The authors thank the hospitality and the generosity of the FIM at ETH Zurich and the Division of Mathematical Sciences of the Nanyang Technological University, Singapore, where a significant portion of the results in this paper were obtained.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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