Symbolic extensions and continuity properties of the entropy

David Burguet (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

In this short note we give a new presentation of the entropy theory of symbolic extensions. Then we deduce from the main results of this theory some continuity properties of the entropy regarding the smoothness of the dynamical system. We also prove that generic continuous interval maps have nowhere continuous entropy function.

Domaines: Systèmes dynamiques [math.DS]

David Burguet. Symbolic extensions and continuity properties of the entropy. 2010. ⟨hal-00578303⟩