The Decay Rate of Patterson-Sullivan Measures with Potential Functions and Critical Exponents
Abstract
Basing upon the recent development of the Patterson-Sullivan measures with a Hölder continuous nonzero potential function, we use tools of both dynamics of geodesic flows and geometric properties of negatively curved manifolds to present a new formula illustrating the relation between the exponential decay rate of Patterson-Sullivan measures with a Hölder continuous potential function and the corresponding critical exponent.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2018
- DOI:
- 10.48550/arXiv.1810.11133
- arXiv:
- arXiv:1810.11133
- Bibcode:
- 2018arXiv181011133F
- Keywords:
-
- Mathematics - Dynamical Systems
- E-Print:
- 11 pages