Growth of degrees of integrable mappings

DOI10.1080/10236198.2010.510137zbMath1238.39003arXiv1005.2065OpenAlexW2056897898MaRDI QIDQ2881918

Peter H. van der Kamp

Publication date: 3 May 2012

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

Full work available at URL: https://arxiv.org/abs/1005.2065

zbMATH Keywords

polynomial growthintegrable mappingsalgebraic entropylattice equationslattice Korteweg-de Vries equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Discrete version of topics in analysis (39A12)

Related Items (6)

QRT maps and related Laurent systems ⋮ Algebraic entropy of (integrable) lattice equations and their reductions ⋮ Elementary exact calculations of degree growth and entropy for discrete equations ⋮ Linear degree growth in lattice equations ⋮ From discrete integrable equations to Laurent recurrences ⋮ Calculation of algebraic entropies of d-PIV and d-PV

Cites Work

• Discrete Painlevé I and singularity confinement in projective space
• Growth and integrability in the dynamics of mappings
• Integrable lattice equations and their growth properties
• Singularity, complexity, and quasi-integrability of rational mappings
• Algebraic entropy
• Singularity confinement and algebraic entropy: the case of the discrete Painlevé equations
• Algebraic entropy of birational maps with invariant curves
• Initial value problems for lattice equations
• Dynamics of complexity of intersections
• Diophantine integrability
• On the complexity of some birational transformations
• Searching for integrable lattice maps using factorization

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