Finding eigenvalues of self-maps with the Kronecker canonical form Conference Paper

Author(s): Ethier, Marc; Jablonski, Grzegorz; Mrozek, Marian
Title: Finding eigenvalues of self-maps with the Kronecker canonical form
Title Series: PROMS
Affiliation IST Austria
Abstract: Recent research has examined how to study the topological features of a continuous self-map by means of the persistence of the eigenspaces, for given eigenvalues, of the endomorphism induced in homology over a field. This raised the question of how to select dynamically significant eigenvalues. The present paper aims to answer this question, giving an algorithm that computes the persistence of eigenspaces for every eigenvalue simultaneously, also expressing said eigenspaces as direct sums of “finite” and “singular” subspaces.
Keywords: persistent homology; Computational topology; self-maps; matrix pencils; Kronecker canonical form
Conference Title: ACA: Applications of Computer Algebra
Volume: 198
Publisher: Springer  
Date Published: 2017-07-27
Start Page: 119
End Page: 136
Sponsor: FP7-ICT-318493-STREP, Polish MNiSzW grant Nr 2621/7.PR/12/2013/2, National Science Centre (Poland) grant DEC-2013/09/N/ST6/02995
DOI: 10.1007/978-3-319-56932-1_8
Open access: no
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