The Decay Rate of Patterson-Sullivan Measures with Potential Functions and Critical Exponents
Dynamical Systems
2018-10-30 v2
Abstract
Basing upon the recent development of the Patterson-Sullivan measures with a H\"older 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 H\"older continuous potential function and the corresponding critical exponent.
Keywords
Cite
@article{arxiv.1810.11133,
title = {The Decay Rate of Patterson-Sullivan Measures with Potential Functions and Critical Exponents},
author = {Ziqiang Feng and Fei Liu and Fang Wang},
journal= {arXiv preprint arXiv:1810.11133},
year = {2018}
}
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11 pages