Mathematics – Dynamical Systems
Scientific paper
2006-12-20
Mathematics
Dynamical Systems
Scientific paper
Geometric models and Teichm\"uller structures have been introduced for the space of smooth expanding circle endomorphisms and for the space of uniformly symmetric circle endomorphisms. The latter one is the completion of the previous one under the Techm\"uller metric. Moreover, the spaces of geometric models as well as the Teichm\"uller spaces can be described as the space of H\"older continuous scaling functions and the space of continuous scaling functions on the dual symbolic space. The characterizations of these scaling functions have been also investigated. The Gibbs measure theory and the dual Gibbs measure theory for smooth expanding circle dynamics have been viewed from the geometric point of view. However, for uniformly symmetric circle dynamics, an appropriate Gibbs measure theory is unavailable, but a dual Gibbs type measure theory has been developed for the uniformly symmetric case. This development extends the dual Gibbs measure theory for the smooth case from the geometric point of view. In this survey article, We give a review of these developments which combines ideas and techniques from dynamical systems, quasiconformal mapping theory, and Teichm\"uller theory. There is a measure-theoretical version which is called $g$-measure theory and which corresponds to the dual geometric Gibbs type measure theory. We briefly review it too.
Jiang Yunping
No associations
LandOfFree
Function Models for Teichmüller Spaces and Dual Geometric Gibbs Type Measure Theory for Circle Dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Function Models for Teichmüller Spaces and Dual Geometric Gibbs Type Measure Theory for Circle Dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Function Models for Teichmüller Spaces and Dual Geometric Gibbs Type Measure Theory for Circle Dynamics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-242489