Algebraic entropy for hex systems
arXiv:2311.01359 · doi:10.1088/1361-6544/ad88cd
Abstract
Hex systems were recently introduced [A. P. Kels. Integrable systems on hexagonal lattices and consistency on polytopes with quadrilateral and hexagonal faces. 2022. arXiv:2205.02720 [math-ph]] as systems of equations defined on two-dimensional honeycomb lattices. We give a definition of algebraic entropy for such systems and use it to check the integrability of specific examples.
25 pages, 7 figures, 10 tables, corrected typos, added and updated references
References in corpus (24)
- Algebraic entropy
- Singularity confinement and chaos in discrete systems
- Lax pair for the Adler (lattice Krichever-Novikov) System
- Soliton Solutions for ABS Lattice Equations: I Cauchy Matrix Approach
- Multidimensional Quadrilateral Lattices are Integrable
- Discrete analogues of the Liouville equation
- Soliton Solutions for ABS Lattice Equations II: Casoratians and Bilinearization
- Integrable lattice equations and their growth properties
- Elliptic gamma-function and multi-spin solutions of the Yang-Baxter equation
- Soliton solutions for Q3
- Algebraic entropy and the space of initial values for discrete dynamical systems
- Algebraic Entropy for lattice equations
- What is integrability of discrete variational systems?
- Symmetries and integrability of discrete equations defined on a black-white lattice
- Weak Lax pairs for lattice equations
- On the algebraic structure of rational discrete dynamical systems
- On the Lagrangian structure of integrable quad-equations
- Darboux Integrability of Trapezoidal and Families of Lattice Equations II: General Solutions
- Darboux integrability of trapezoidal and families of lattice equations I: First integrals
- Interaction-round-a-face and consistency-around-a-face-centered-cube
- Extended Z-invariance for integrable vector and face models and multi-component integrable quad equations
- Degree growth of lattice equations defined on a 3x3 stencil
- Algebraic entropy for systems of quad equations
- Integrable systems on hexagonal lattices and consistency on polytopes with quadrilateral and hexagonal faces