@article{675e343b6b954f9890f654b037479c20,
title = "Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem",
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{\"o}lder exponent-based criteria.",
author = "Lyudmila Grigoryeva and Allen Hart and Ortega, {Juan Pablo}",
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 Universit{\"a}t 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. ",
year = "2021",
month = jun,
day = "3",
doi = "10.1103/PhysRevE.103.062204",
language = "English",
volume = "103",
journal = "Physical Review E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "6",
}