Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Franks' Lemma for C^2-Man\'e Perturbations of Riemannian Metrics and
  Applications to Persistence   Given a compact Riemannian manifold, we prove a uniform Franks' lemma at
second order for geodesic flows and apply the result in persistence theory.

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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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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: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: stat