Algebraic Entropy of Birational Maps with Invariant Curves

Abstract

The relevance of the algebraic entropy in the study of birational discrete time dynamical systems highlights the need to relate it to other characteristics of these systems. In this letter, two complementary proofs are given that the foliation of the space by invariant curves implies that the algebraic entropy is zero.

11 pages, no figure

References in corpus (4)

• Algebraic entropy
• Vacuum curves, classical integrable systems in discrete space-time and statistical physics
• Integrable mappings and polynomial growth
• Towards Three-Dimensional Bethe Ansatz

Cited by in corpus (12)

• Integrable lattice equations and their growth properties
• Discrete integrable systems and Poisson algebras from cluster maps
• Algebraic entropy and the space of initial values for discrete dynamical systems
• A classification of four-state spin edge Potts models
• Singularity confinement and algebraic integrability
• Bi-rational maps in four dimensions with two invariants
• Rational Maps with Invariant Surfaces
• Algebraic entropy of sign-stable mutation loops
• Degree-growth of monomial maps
• Integrability of $n$-dimensional dynamical systems of type $E_7^{(1)}$ and $E_8^{(1)}$
• QRT maps and related Laurent systems
• On the degree growth of iterated birational maps