Bi-rational maps in four dimensions with two invariants
arXiv:1907.00746 · doi:10.1088/1751-8121/ab72ad
Abstract
In this paper we present a class of four-dimensional bi-rational maps with two invariants satisfying certain constraints on degrees. We discuss the integrability properties of these maps from the point of view of degree growth and Liouville integrability.
arXiv comment26 pages. arXiv admin note: text overlap with arXiv:1808.04942
References in corpus (9)
- Algebraic entropy
- Geometric properties of Kahan's method
- Singularity, complexity, and quasi--integrability of rational mappings
- Algebraic entropy and the space of initial values for discrete dynamical systems
- Integrability properties of Kahan's method
- Algebraic Entropy of Birational Maps with Invariant Curves
- A classification of four-state spin edge Potts models
- Poisson brackets of mappings obtained as (q,-p) reductions of lattice equations
- On the inverse problem of the discrete calculus of variations