From discrete integrable equations to Laurent recurrences

DOI10.1080/10236198.2016.1142980zbMath1353.39013OpenAlexW2278350229MaRDI QIDQ2816620

K. Hamad, Peter H. van der Kamp

Publication date: 25 August 2016

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236198.2016.1142980

zbMATH Keywords

integrabilityrational difference equationsLaurent propertyultra-discretizationSomos sequencesrecursive factorizationgeneralized Lyness equation

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Discrete version of topics in analysis (39A12) Multiplicative and other generalized difference equations (39A20)

Related Items (8)

Somos-4 and Somos-5 are arithmetic divisibility sequences ⋮ QRT maps and related Laurent systems ⋮ Some integrable maps and their Hirota bilinear forms ⋮ Linear relations for Laurent polynomials and lattice equations ⋮ On the coprimeness property of discrete systems without the irreducibility condition ⋮ Duality for discrete integrable systems II ⋮ Investigation into the role of the Laurent property in integrability ⋮ From discrete integrable equations to Laurent recurrences

Uses Software

• OEIS

Cites Work

• Laurent phenomenon algebras
• Laurent phenomenon sequences
• Discrete integrable systems and Poisson algebras from cluster maps
• Cluster mutation-periodic quivers and associated Laurent sequences
• The Laurent phenomenon
• Integrability in a discrete world
• Magic determinants of Somos sequences and theta functions
• Growth and integrability in the dynamics of mappings
• An integer sequence from a rational recursion
• Singularity, complexity, and quasi-integrability of rational mappings
• Algebraic entropy
• Integrable mappings and soliton equations. II
• Cluster algebras in algebraic Lie theory
• Singularity confinement and algebraic entropy: the case of the discrete Painlevé equations
• Singularity confinement for maps with the Laurent property
• Primitive divisors of elliptic divisibility sequences
• Tilting theory and cluster combinatorics.
• Cluster algebras I: Foundations
• From discrete integrable equations to Laurent recurrences
• Growth of degrees of integrable mappings
• Irreducibility and co-primeness as an integrability criterion for discrete equations
• Discrete Painlevé equations from Y-systems
• Bilinear discrete Painleve equations
• Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences
• Cluster ensembles, quantization and the dilogarithm
• Dynamics of complexity of intersections
• Darboux and binary Darboux transformations for the nonautonomous discrete KP equation
• Primes generated by elliptic curves
• ELLIPTIC CURVES AND QUADRATIC RECURRENCE SEQUENCES
• How to generate as many Somos-like miracles as you wish^†
• Birational maps that send biquadratic curves to biquadratic curves
• On the algebraic structure of rational discrete dynamical systems
• Sigma function solution of the initial value problem for Somos 5 sequences
• A novelnth order difference equation that may be integrable
• Dynamics of the third order Lyness' difference equation
• Degree-growth of monomial maps
• Ultradiscrete QRT maps and tropical elliptic curves
• RECURRENCE RELATIONS FOR ELLIPTIC SEQUENCES: EVERY SOMOS 4 IS A SOMOS LOWERCASE $k$
• Memoir on Elliptic Divisibility Sequences

This page was built for publication: From discrete integrable equations to Laurent recurrences