Elementary exact calculations of degree growth and entropy for discrete equations

Second-order discrete equations are studied over the field of rational functions [Formula: see text] , where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations that arise in singularity confineme...

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Detalles Bibliográficos
Autor principal: Halburd, R. G.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2017
Materias:
Research Articles
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5454346/
https://www.ncbi.nlm.nih.gov/pubmed/28588401
http://dx.doi.org/10.1098/rspa.2016.0831
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author Halburd, R. G.
author_facet Halburd, R. G.
author_sort Halburd, R. G.
collection PubMed
description Second-order discrete equations are studied over the field of rational functions [Formula: see text] , where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations that arise in singularity confinement analysis, even when the singularities are not confined. This produces elementary yet rigorous entropy calculations.
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spelling pubmed-54543462017-06-06 Elementary exact calculations of degree growth and entropy for discrete equations Halburd, R. G. Proc Math Phys Eng Sci Research Articles Second-order discrete equations are studied over the field of rational functions [Formula: see text] , where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations that arise in singularity confinement analysis, even when the singularities are not confined. This produces elementary yet rigorous entropy calculations. The Royal Society Publishing 2017-05 2017-05-03 /pmc/articles/PMC5454346/ /pubmed/28588401 http://dx.doi.org/10.1098/rspa.2016.0831 Text en © 2017 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Research Articles
Halburd, R. G.
Elementary exact calculations of degree growth and entropy for discrete equations
title Elementary exact calculations of degree growth and entropy for discrete equations
title_full Elementary exact calculations of degree growth and entropy for discrete equations
title_fullStr Elementary exact calculations of degree growth and entropy for discrete equations
title_full_unstemmed Elementary exact calculations of degree growth and entropy for discrete equations
title_short Elementary exact calculations of degree growth and entropy for discrete equations
title_sort elementary exact calculations of degree growth and entropy for discrete equations
topic Research Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5454346/
https://www.ncbi.nlm.nih.gov/pubmed/28588401
http://dx.doi.org/10.1098/rspa.2016.0831
work_keys_str_mv AT halburdrg elementaryexactcalculationsofdegreegrowthandentropyfordiscreteequations

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