摘要
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.
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.
基金
partially supported by NSFC(Grant Nos.11571207 and 11871045)
the third author is partially supported by NSFC(Grant No.11871045)
by the State Scholarship Fund from China Scholarship Council(CSC)
