Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse periodic shadowing properties   We consider inverse periodic shadowing properties of discrete dynamical
systems generated by diffeomorphisms of closed smooth manifolds. We show that
the $C^1$-interior of the set of all diffeomorphisms having so-called inverse
periodic shadowing property coincides with the set of $\Omega$-stable
diffeomorphisms. The equivalence of Lipschitz inverse periodic shadowing
property and hyperbolicity of the closure of all periodic points is proved.
Besides, we prove that the set of all diffeomorphisms that have Lipschitz
inverse periodic shadowing property and whose periodic points are dense in the
nonwandering set coincides with the set of Axiom A diffeomorphisms.

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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org