Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of infinitely many invariant Reeb orbits   In this article we extend results of Grove and Tanaka on the existence of
isometry-invariant geodesics to the setting of Reeb flows and strict
contactomorphisms. Specifically, we prove that if M is a closed connected
manifold with the property that the Betti numbers of the free loop space are
asymptotically unbounded then for every fibrewise star-shaped hypersurface in
the cotangent bundle of M and every strict contactomorphism of that
hypersurface which is contact-isotopic to the identity, there are infinitely
many invariant Reeb orbits.

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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg