Algebraic dynamics: what values for the algebraic entropy ?

Abstract:

To any dynamical system with a rational evolution, we may associate a global index of complexity, its algebraic entropy. Integrable systems have a vanishing entropy, and this is now commonly used as an integrability detector. As the entropy was conjectured to be the logarithm of an algebraic integer, it cannot assume arbitrary values. It is then natural to ask: what is the range of values of the entropy ? We will mainly address this question.