Teichmüller Structures and Dual Geometric Gibbs Type Measure Theory for Continuous Potentials

Details Teichmüller Structures and Dual Geometric Gibbs Type Measure Theory for Continuous Potentials Teichmüller Structures and Dual Geometric Gibbs Type Measure Theory for Continuous Potentials

2008-04-18

arxiv.org/abs/0804.3104v3

Mathematics

Dynamical Systems

Scientific paper

The Gibbs measure theory for smooth potentials is an old and beautiful subject and has many important applications in modern dynamical systems. For continuous potentials, it is impossible to have such a theory in general. However, we develop a dual geometric Gibbs type measure theory for certain continuous potentials in this paper following some ideas and techniques from Teichm\"uller theory for Riemann surfaces. Furthermore, we prove that the space of those continuous potentials has a Teichm\"uller structure. Moreover, this Teichm\"uller structure is a complete structure and is the completion of the space of smooth potentials under this Teichm\"uller structure. Thus our dual geometric Gibbs type theory is the completion of the Gibbs measure theory for smooth potentials from the dual geometric point of view.

Affiliated with

Also associated with

No associations

Rating

Teichmüller Structures and Dual Geometric Gibbs Type Measure Theory for Continuous Potentials 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 Teichmüller Structures and Dual Geometric Gibbs Type Measure Theory for Continuous Potentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Teichmüller Structures and Dual Geometric Gibbs Type Measure Theory for Continuous Potentials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-651400