Topological Properties of Periodic and Chaotic Attractors

Abstract

Many topological methods have been developed to analyze topological properties of different types of attractors of a dynamical systems. Using different tools in topological data analysis, we can describe the shape of attractors of system. In this chapter, we use some of these topological tools such as persistence diagram or Barcode diagram to demonstrate different patterns in the structure of the system and to count the number of loops and holes in data. Also, we use simplicial complexes to describe the topology of the data at different scales.