Computability and the morphological complexity of some dynamics on continuous domains

Mathieu Hoyrup (1) , Arda Kolçak (1) , Giuseppe Longo (1)

1 LIENS - Laboratoire d'informatique de l'école normale supérieure

The partially ordered set of compact intervals provides a convenient embedding space for the analysis of some Dynamical Systems. Crucial dynamical properties are transferred to it, while allowing an investigation of stability and chaoticity, in terms of computability, in particular in the presence of singularities. We will survey some results which display the connections between the geometric complexity of the dynamics and computability issues, as well as new relations between dynamic predictability and effective decidability.

Mots clés: Computability over continuous domains; Decidability; Unpredictability; Chaotic dynamics; Singularities; Shadowing

Domaines: Informatique [cs]; Mathématiques [math]

Mathieu Hoyrup, Arda Kolçak, Giuseppe Longo. Computability and the morphological complexity of some dynamics on continuous domains. Theoretical Computer Science, 2008, 398 (1-3), pp.170-182. ⟨10.1016/j.tcs.2008.01.048⟩. ⟨hal-03319898⟩