| Abstract: |
| A key tool in comparing and classifying dynamical systems is the notion of topological conjugacy. In this talk, we consider the problem of testing (semi-)topological conjugacy between two trajectories arising from unknown dynamical systems when only finite samples of these trajectories are available. We will discuss a range of tests inspired by methods from topological data analysis and present various numerical examples demonstrating their effectiveness.
Moreover, we will show that these methods can be applied to determine the optimal embedding dimension, referring to the well-known Takens` Embedding Theorem, which provides a theoretical framework for time series analysis in a wide range of applications.
The talk is based on joint work with Pawel Dlotko (Dioscuri Centre in TDA), Michal Lipinski (IST Austria), and Marta Marszewska (Gdansk University of Technology and Dioscuri Centre in TDA). |
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