Publikation: Chaos on compact manifolds : Differentiable synchronizations beyond the Takens theorem
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2021
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Physical Review E. American Physical Society (APS). 2021, 103(6), 062204. ISSN 2470-0045. eISSN 2470-0053. Available under: doi: 10.1103/PhysRevE.103.062204
Zusammenfassung
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.
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GRIGORYEVA, Lyudmila, Allen HART, Juan-Pablo ORTEGA, 2021. Chaos on compact manifolds : Differentiable synchronizations beyond the Takens theorem. In: Physical Review E. American Physical Society (APS). 2021, 103(6), 062204. ISSN 2470-0045. eISSN 2470-0053. Available under: doi: 10.1103/PhysRevE.103.062204BibTex
@article{Grigoryeva2021Chaos-54318,
year={2021},
doi={10.1103/PhysRevE.103.062204},
title={Chaos on compact manifolds : Differentiable synchronizations beyond the Takens theorem},
number={6},
volume={103},
issn={2470-0045},
journal={Physical Review E},
author={Grigoryeva, Lyudmila and Hart, Allen and Ortega, Juan-Pablo},
note={Article Number: 062204}
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<dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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