Hans-Henrik Rugh: The problem of conjugacy
Abstract:
Interesting objects in dynamical systems often appear quite irregular. On the other hand, characteristic exponents or thermodynamic averages, often turn out to be as regular as the dynamical system in question. About a decade ago, Ruelle suggested to view and explain such phenomena by considering it as a problem of `conjugacy'. In this seminar we consider as an instructive example the Hausdorff dimension of Julia-sets of rational map. An old theorem, also by Ruelle, states that the Hausdorff dimension depends real-analytically on the map in the uniformly hyperbolic case. We will here revisit this result by applying the newer concepts suggested by Ruelle.