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Communications in Mathematical Physics

, Volume 275, Issue 3, pp 721–748 | Cite as

Complexity for Extended Dynamical Systems

  • Claudio BonannoEmail author
  • Pierre Collet
Article

Abstract

We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, ϵ-entropy and topological entropy per unit time and volume have been introduced previously. In this paper we use the notion of Kolmogorov complexity to introduce, for extended dynamical systems, a notion of complexity per unit time and volume which plays the same role as the metric entropy for classical dynamical systems. We introduce this notion as an almost sure limit on orbits of the system. Moreover we prove a kind of variational principle for this complexity.

Keywords

Probability Measure Open Covering Unbounded Domain Topological Entropy Kolmogorov Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Dipartimento di Matematica ApplicataUniversità di PisaPisaItaly
  2. 2.Centre de Physique Théorique, École PolytechniqueCNRS UMR 7644Palaiseau CedexFrance

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