Monday 27 Jan 2014: Transience and multifractal analysis
Thomas Jordan - University of Bristol
Harrison 101 15:00-16:00
Joint work with Godofredo Iommi and Mike Todd. Multifractal analysis involves decomposing a set into level sets where a suitable locally defined quantity is constant. In this talk the fractal property studied will be Hausdorff dimension and the local quantity will be Birkhoff average for a potential for an expanding interval map. In the case when the interval map has a finite Markov partition then this problem is well understood. The Hausdorff dimension of the level sets correspond to the dimension of a certain ergodic measure (i.e. a variational principle holds). It is also possible to give an implicit formula for this dimension involving the topological pressure. We will consider the case of when the partition is countable. In this setting the situation is much more complicated and the variational principle may not hold. In particular we will give an example where dissipative behaviour occurs and no such variational occurs. However we will also show that if we restrict attention to recurrent points then a similar variational principle to the case of a finite Markov partition occurs and that the Hausdorff dimension can be connected to the Gurevic pressure.