Discrete Conley Index for Zero-dimensional Basic Sets
Ketty A. de Rezende, Mariana G. Villapouca

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.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Molecular spectroscopy and chirality · Quantum chaos and dynamical systems
