Calculating the algebraic entropy of mappings with unconfined singularities. Issue 1 (6th June 2018)

• Record Type: Journal Article
• Authors: Ramani, A; Grammaticos, B; Willox, R; Mase, T; Satsuma, J
• Is Part Of: Journal of integrable systems. Volume 3:Issue 1(2018)
• Publication Date: 2018-06-06
• Subjects: 02.30.Ik -- 05.45.Yv; mappings -- integrability -- deautonomization -- singularities -- algebraic entropy; Mathematics -- Periodicals; 510
• DOI: 10.1093/integr/xyy006
• Languages: English
• ISSNs: 2058-5985

Abstract

Abstract: We present a method for calculating the dynamical degree of a mapping with unconfined singularities. It is based on a method introduced by Halburd for the computation of the growth of the iterates of a rational mapping with confined singularities. In particular, we show through several examples how simple calculations, based on the singularity patterns of the mapping, allow one to obtain the exact value of the dynamical degree for non-integrable mappings that do not possess the singularity confinement property. We also study linearizable mappings with unconfined singularities to show that in this case our method indeed yields zero algebraic entropy. Communicated by: Kenji Kajiwara