Chaos on compact manifolds: differentiable synchronizations beyond the Takens theorem

• Main Authors: Grigoryeva, Lyudmila, Hart, Allen, Ortega, Juan-Pablo
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics; Generalized Synchronization; Systems
• Online Access: https://hdl.handle.net/10356/154971
• Institution: Nanyang Technological University

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.