Topological Analysis of Recurrent Systems
Primož Škraba, Vin de Silva, Mikael Vejdemo‐Johansson · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 2012
We propose a new framework for the experimental study of periodic, quasi- periodic and recurrent dynamical systems. These behaviors express themselves as topological features which we detect using persistent cohomology. The result- ing 1-cocycles yield circle-valued coordinates associated to the recurrent behavior. We demonstrate how to use these coordinates to perform fundamental tasks like period recovery and parameter choice for delay embeddings.