Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: V.I. Arnold's "Global" KAM Theorem and geometric measure estimates   This paper continues the discussion started in [CK19] concerning Arnold's
legacy on classical KAM theory and (some of) its modern developments. We prove
a detailed and explicit `global' Arnold's KAM Theorem, which yields, in
particular, the Whitney conjugacy of a non-degenerate, real-analytic,
nearly-integrable Hamiltonian system to an integrable system on a closed,
nowhere dense, positive measure subset of the phase space. Detailed measure
estimates on the Kolmogorov's set are provided in the case the phase space is:
(A) a uniform neighborhood of an arbitrary (bounded) set times the d-torus and
(B) a domain with $C^2$ boundary times the d-torus. All constants are
explicitly given.

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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th