Discrete Conley Index for Zero-dimensional Basic Sets

TL;DR

This paper introduces a method to compute the discrete Conley index for zero-dimensional basic sets using structure matrices, providing a classification based on Jordan form to understand their topological dynamics.

Contribution

It presents a new theorem for computing the discrete Conley index and classifies the index via Jordan form, advancing the understanding of zero-dimensional basic sets.

Findings

Computed the discrete Conley index using structure matrices.

Classified the index through Jordan real form.

Linked the index to dynamical information of basic sets.

Abstract

A theorem is established where the computation of the discrete Conley index for zero dimensional basic sets is given with respect to the dynamical information contained in the associated structure matrices. A classification of the reduced homology Conley index of a zero dimensional basic set in terms of its Jordan real form is presented.