On the algebraic structure of rational discrete dynamical systems

Abstract

We show how singularities shape the evolution of rational discrete dynamical systems. The stabilisation of the form of the iterates suggests a description providing among other things generalised Hirota form, exact evaluation of the algebraic entropy as well as remarkable polynomial factorisation properties. We illustrate the phenomenon explicitly with examples covering a wide range of models.

References in corpus (1)

• Laurent Polynomials and Superintegrable Maps

Cited by in corpus (9)

• Some integrable maps and their Hirota bilinear forms
• Rational Maps with Invariant Surfaces
• Algebraic entropy of an extended Hietarinta-Viallet equation
• Coalgebra symmetry for discrete systems
• Algebraic entropy for face-centered quad equations
• An exercise in experimental mathematics: calculation of the algebraic entropy of a map
• Degree growth of lattice equations defined on a 3x3 stencil
• Algebraic entropy for systems of quad equations
• Algebraic entropy for hex systems