Dynamical Similarity of Time-Series

A key concept in comparison and classification of dynamical systems is the notion of topological conjugacy. In the talk we will consider a problem of testing topological (semi-)conjugacy of two trajectories coming from unknown dynamical systems when only finite samples of those trajectories are given. A number of tests and various numerical examples indicating their scalability and robustness will be discussed. In addition, we will see how presented methods apply for searching of sufficient embedding dimension, mentioned in Takens’ Embedding Theorem, which provides a theoretical framework for time series analysis in various applications.  

This is a joint work with Paweł Dłotko (Dioscuri Centre in TDA, Warsaw) and Michał Lipiński (IST Austria).