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Fitting ideals for finitely presented algebraic dynamical systems

Einsiedler, M.; Ward, T.

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Authors

M. Einsiedler

T. Ward



Abstract

We consider a class of algebraic dynamical systems introduced by Kitchens and Schmidt. Under a weak finiteness condition - the Descending Chain Condition - the dual modules have finite resentations. Using methods from commutative algebra we show how the dynamical properties of the system may be deduced from the Fitting ideals of a finite free resolution of the finitely presented module. The entropy and expansiveness are shown to depend only on the initial Fitting ideal (and certain multiplicity data) which gives an easy computation: in particular, no syzygy modules need to be computed. For "square" presentations (in which the number of generators is equal to the number of relations) all the dynamics is visible in the initial Fitting ideal and certain multiplicity data, and we show how the dynamical properties and periodic point behaviour may be deduced from the determinant of the matrix of relations.

Citation

Einsiedler, M., & Ward, T. (2000). Fitting ideals for finitely presented algebraic dynamical systems. Aequationes Mathematicae, 60(1-2), 57-71. https://doi.org/10.1007/s000100050135

Journal Article Type Article
Publication Date Jan 1, 2000
Deposit Date Oct 12, 2012
Publicly Available Date Mar 28, 2024
Journal Aequationes Mathematicae
Print ISSN 0001-9054
Electronic ISSN 1420-8903
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 60
Issue 1-2
Pages 57-71
DOI https://doi.org/10.1007/s000100050135

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Copyright Statement
The original publication is available at www.springerlink.com




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