Persistence of the Conley Index in Combinatorial Dynamical Systems

03/12/2020 ∙ by Tamal K. Dey, et al. ∙ 0

A combinatorial framework for dynamical systems provides an avenue for connecting classical dynamics with data-oriented, algorithmic methods. Combinatorial vector fields introduced by Forman and their recent generalization to multivector fields have provided a starting point for building such a connection. In this work, we strengthen this relationship by placing the Conley index in the persistent homology setting. Conley indices are homological features associated with so-called isolated invariant sets, so a change in the Conley index is a response to perturbation in an underlying multivector field. We show how one can use zigzag persistence to summarize changes to the Conley index, and we develop techniques to capture such changes in the presence of noise. We conclude by developing an algorithm to track features in a changing multivector field.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 10

page 11

page 12

page 14

page 21

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.