Singularity confinement and chaos in two-dimensional discrete systems

Abstract

We present a quasi-integrable two-dimensional lattice equation: i.e., a partial difference equation which satisfies a criterion of integrability, singularity confinement, although it has a chaotic aspect in the sense that the degrees of its iterates exhibit exponential growth. By systematic reduction to one-dimensional systems, it gives a hierarchy of ordinary difference equations with confined singularities, but with positive algebraic entropy including a generalized form of the Hietarinta-Viallet mapping. We believe that this is the first example of such quasi-integrable equations defined over a two-dimensional lattice.

10 pages, 1 figure

References in corpus (4)

• Singularity confinement and full-deautonomisation: a discrete integrability criterion
• The redemption of singularity confinement
• Algebraic entropy of an extended Hietarinta-Viallet equation
• Integrability criterion in terms of coprime property for the discrete Toda equation

Cited by in corpus (7)

• Full-deautonomisation of a lattice equation
• Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation
• On the Coprimeness Property of Discrete Systems without the Irreducibility Condition
• Nonequilibrium physics in integrable systems and spin-flip non-invariant conserved quantities
• Coprimeness-preserving discrete KdV type equation on an arbitrary dimensional lattice
• Algebraic entropy of a multi-term recurrence of the Hietarinta-Viallet type
• Detecting discrete integrability: the singularity approach