Chaos on compact manifolds : Differentiable synchronizations beyond the Takens theorem

Grigoryeva, Lyudmila; Hart, Allen; Ortega, Juan-Pablo

Chaos on compact manifolds : Differentiable synchronizations beyond the Takens theorem

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Datum

2021

Autor:innen

Grigoryeva, Lyudmila

Hart, Allen

Ortega, Juan-Pablo

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Physical Review E. American Physical Society (APS). 2021, 103(6), 062204. ISSN 2470-0045. eISSN 2470-0053. Available under: doi: 10.1103/PhysRevE.103.062204

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.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

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.103.062204

BibTex

@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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