The redemption of singularity confinement

Abstract

We present a novel way to apply the singularity confinement property as a discrete integrability criterion. We shall use what we call a full deautonomisation approach, which consists in treating the free parameters in the mapping as functions of the independent variable, applied to a mapping complemented with terms that are absent in the original mapping but which do not change the singularity structure. We shall show, on a host of examples including the well-known mapping of Hietarinta-Viallet, that our approach offers a way to compute the algebraic entropy for these mappings exactly, thereby allowing one to distinguish between the integrable and non-integrable cases even when both have confined singularities.

7 pages

References in corpus (3)

• Singularity confinement and chaos in discrete systems
• Diophantine Integrability
• Algebraic entropy and the space of initial values for discrete dynamical systems

Cited by in corpus (6)

• Singularity confinement and full-deautonomisation: a discrete integrability criterion
• Singularity confinement and chaos in two-dimensional discrete systems
• Algebraic entropy of an extended Hietarinta-Viallet equation
• A systematic method for constructing discrete Painlevé equations in the degeneration cascade of the E${}_8$ group
• Coprimeness-preserving discrete KdV type equation on an arbitrary dimensional lattice
• Discrete Painlevé equations from singularity patterns: the asymmetric trihomographic case