descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 10 Dec 2015Embargo end date: 01 Jan 2015Publisher:IOP PublishingJournal:Journal of Physics A: Mathematical and Theoretical, volume 49, page 02LT01 (issn: 1751-8113, eissn: 1751-8121,

Authors: Hone, A. N. W.; Ragnisco, Orlando; Zullo, Federico;

doi: 10.1088/1751-8113/49/2/02lt01 , 10.48550/arxiv.1508.01440

arXiv: http://arxiv.org/abs/1508.01440

handle: 11379/499501 , 11590/301872

Algebraic entropy for algebraic maps

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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.

17 pages

Related Organizations

National Institute for Nuclear Physics
Italy
Roma Tre University
Italy
University of Kent
United Kingdom
University of Brescia
Italy

Keywords

QA801, Nonlinear Sciences - Exactly Solvable and Integrable Systems, algebraic entropy; algebraic maps; integrability tests; Mathematical Physics; Physics and Astronomy (all); Statistical and Nonlinear Physics; Modeling and Simulation; Statistics and Probability, FOS: Physical sciences, QA564, Chaotic Dynamics (nlin.CD), Exactly Solvable and Integrable Systems (nlin.SI), Nonlinear Sciences - Chaotic Dynamics, QC20

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