• Pierre Collet
  • Jean-Pierre Eckmann
Part of the Theoretical and Mathematical Physics book series (TMP)


In Sect. 3.2 we already addressed the subject of fuzzy knowledge from a purely topological point of view. Here, we come back to this idea, but now, we also connect it to the notion of invariant measure. That is, we account (in particular in the natural case of the Physical measure) for how often (or how long) a trajectory stays in a particular region. One can ask how much information this gives us about the long-time dynamics of the system and the variability of the set of orbits. The main difference with the topological entropy is that we are not going to consider all trajectories but only those “typical” for a given measure.


Lyapunov Exponent Invariant Measure Hausdorff Dimension Full Measure Topological Entropy 
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Copyright information

© Springer 2006

Authors and Affiliations

  • Pierre Collet
    • 1
  • Jean-Pierre Eckmann
    • 2
  1. 1.Center of Theoretical Physics École PolytechniquePalaiseauFrance
  2. 2.Department of Theoretical Physics and Mathematics SectionUniversity of GenevaSwitzerland

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