Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Decay Rate of Patterson-Sullivan Measures with Potential Functions
  and Critical Exponents   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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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph