Chaos on compact manifolds: differentiable synchronizations beyond the Takens theorem
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, reconstruct...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2022
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| Online Access: | https://hdl.handle.net/10356/154971 |
| _version_ | 1826120041420029952 |
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| author | Grigoryeva, Lyudmila Hart, Allen Ortega, Juan-Pablo |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Grigoryeva, Lyudmila Hart, Allen Ortega, Juan-Pablo |
| author_sort | Grigoryeva, Lyudmila |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T05:10:04Z |
| format | Journal Article |
| id | ntu-10356/154971 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:10:04Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1549712023-02-28T20:06:54Z Chaos on compact manifolds: differentiable synchronizations beyond the Takens theorem Grigoryeva, Lyudmila Hart, Allen Ortega, Juan-Pablo School of Physical and Mathematical Sciences Science::Mathematics Generalized Synchronization Systems 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. Published version 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). 2022-05-26T01:09:52Z 2022-05-26T01:09:52Z 2021 Journal Article Grigoryeva, L., Hart, A. & Ortega, J. (2021). Chaos on compact manifolds: differentiable synchronizations beyond the Takens theorem. Physical Review E, 103(6), 062204-. https://dx.doi.org/10.1103/PhysRevE.103.062204 2470-0045 https://hdl.handle.net/10356/154971 10.1103/PhysRevE.103.062204 34271749 2-s2.0-85107685327 6 103 062204 en Physical Review E ©2021 American Physical Society. All rights reserved. This paper was published in Physical Review E and is made available with permission of American Physical Society. application/pdf |
| spellingShingle | Science::Mathematics Generalized Synchronization Systems Grigoryeva, Lyudmila Hart, Allen Ortega, Juan-Pablo Chaos on compact manifolds: differentiable synchronizations beyond the Takens theorem |
| title | Chaos on compact manifolds: differentiable synchronizations beyond the Takens theorem |
| title_full | Chaos on compact manifolds: differentiable synchronizations beyond the Takens theorem |
| title_fullStr | Chaos on compact manifolds: differentiable synchronizations beyond the Takens theorem |
| title_full_unstemmed | Chaos on compact manifolds: differentiable synchronizations beyond the Takens theorem |
| title_short | Chaos on compact manifolds: differentiable synchronizations beyond the Takens theorem |
| title_sort | chaos on compact manifolds differentiable synchronizations beyond the takens theorem |
| topic | Science::Mathematics Generalized Synchronization Systems |
| url | https://hdl.handle.net/10356/154971 |
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