Computability and the morphological complexity of some dynamics on continuous domains

Authors:
Mathieu Hoyrup;Arda Kolçak;Giuseppe Longo
Affiliations:
Laboratoire dInformatique, CNRS et Ecole Normale Supérieure, Paris, France;Laboratoire dInformatique, CNRS et Ecole Normale Supérieure, Paris, France;Laboratoire dInformatique, CNRS et Ecole Normale Supérieure, Paris, France
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

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.