# Algebraic entropy for algebraic maps

Hone, Andrew N.W. (2015) Algebraic entropy for algebraic maps. Journal of Physics A: Mathematical and Theoretical, 49 (2). ISSN 1751-8113. (doi:10.1088/1751-8113/49/2/02LT01) (KAR id:50984)

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http://dx.doi.org/10.1088/1751-8113/49/2/02LT01

## Abstract

We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Backlund transformations.

Item Type: Article 10.1088/1751-8113/49/2/02LT01 [UNSPECIFIED] Cluster algebras with periodicity and discrete dynamics over finite fields Algebraic entropy, algebraic maps, integrability tests. Q Science > QA Mathematics (inc Computing science) > QA564 Algebraic GeometryQ Science > QA Mathematics (inc Computing science) > QA801 Analytic mechanicsQ Science > QC Physics > QC20 Mathematical Physics Faculties > Sciences > School of Mathematics Statistics and Actuarial Science Andrew Hone 14 Oct 2015 11:50 UTC 06 Feb 2020 04:13 UTC https://kar.kent.ac.uk/id/eprint/50984 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-9780-7369