Singularity confinement as an integrability criterion

Abstract

In this paper we present a rigorous method for deciding whether a birational three point mapping that has the singularity confinement property is integrable or not, based only on the structure of its (confined) singularity patterns. We also explain how the exact value of the dynamical degree for such a mapping may be deduced from the singularity patterns.

arXiv comment24 pages, 2 figures

References in corpus (7)

• Singularity confinement and chaos in discrete systems
• Algebraic entropy and the space of initial values for discrete dynamical systems
• Dynamical degrees of birational transformations of projective surfaces
• A geometric approach to singularity confinement and algebraic entropy
• Singularity confinement and full-deautonomisation: a discrete integrability criterion
• Algebraic entropy of an extended Hietarinta-Viallet equation
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Cited by in corpus (7)

• On the singularity structure of the discrete KdV equation
• Algebraic entropy computations for lattice equations: why initial value problems do matter
• On the singularity structure of Kahan discretizations of a class of quadratic vector fields
• Degree growth of lattice equations defined on a 3x3 stencil
• Coprimeness-preserving discrete KdV type equation on an arbitrary dimensional lattice
• Singularity confinement and proliferation of tau functions for a general differential-difference Sawada-Kotera equation
• Growth of Mahler measure and algebraic entropy of dynamics with the Laurent property