On the algebraic structure of rational discrete dynamical systems

We show how singularities shape the evolution of rational discrete dynamical systems. The stabilisation of the form of the iterates suggests a description providing among other things generalised Hirota form, exact evaluation of the algebraic entropy as well as remarkable polynomial factorisation pr...

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Bibliographic Details
Published inarXiv.org
Main Author Viallet, Claude M
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.01.2015
Subjects
Algebra
Dynamical systems
Entropy
Mathematics - Algebraic Geometry
Mathematics - Dynamical Systems
Physics - Exactly Solvable and Integrable Systems
Polynomials
Singularities
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Summary:We show how singularities shape the evolution of rational discrete dynamical systems. The stabilisation of the form of the iterates suggests a description providing among other things generalised Hirota form, exact evaluation of the algebraic entropy as well as remarkable polynomial factorisation properties. We illustrate the phenomenon explicitly with examples covering a wide range of models.
ISSN:2331-8422
DOI:10.48550/arxiv.1501.06384