Algebraic entropy of an extended Hietarinta-Viallet equation

Abstract

We introduce a series of discrete mappings, which is considered to be an extension of the Hietarinta-Viallet mapping with one parameter. We obtain the algebraic entropy for this mapping by obtaining the recurrence relation for the degrees of the iterated mapping. For some parameter values the mapping has a confined singularity, in which case the mapping is equivalent to a recurrence relation between irreducible polynomials. For other parameter values, the mapping does not pass the singularity confinement test. The properties of irreducibility and co-primeness of the terms play crucial roles in the discussion.

22 pages

References in corpus (3)

• On the algebraic structure of rational discrete dynamical systems
• The redemption of singularity confinement
• Integrability criterion in terms of coprime property for the discrete Toda equation

Cited by in corpus (6)

• Investigation into the role of the Laurent property in integrability
• Singularity confinement and full-deautonomisation: a discrete integrability criterion
• Singularity confinement as an integrability criterion
• Singularity confinement and chaos in two-dimensional discrete systems
• Full-deautonomisation of a lattice equation
• Coprimeness-preserving discrete KdV type equation on an arbitrary dimensional lattice