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 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.
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