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Quasi-analytic properties of the KAM curve

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Frank Trujillo

Dynamical Systems · Submitted 30 Dec 2019 · Published version

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, we prove that KAM curves completely characterize the underlying systems.

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arXiv ID1912.13102 (version 2)
Pith ID5PRVSLJ2, Pith's permanent record of this paper and its review
CitationFrank Trujillo. "Quasi-analytic properties of the KAM curve." arXiv:1912.13102 (2019). https://pith.science/paper/5PRVSLJ2
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,133 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.39 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.27 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Classical KAM theory guarantees the existence of a positive measure set of invariant tori for sufficiently smooth non-degenerate near-integrable systems. When seen as a function of the frequency this invariant collection of tori is called the KAM curve of the system. Restricted to analytic regularity, we obtain strong quasi-analyticity properties for these objects. In particular, we prove that KAM curves completely characterize the underlying systems. We also show some of the dynamical implications on systems whose KAM curves share certain common features.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Classical KAM theory guarantees the existence of a positive measure set of invariant tori for sufficiently smooth non-degenerate near-integrable systems. background 1.00 0.04 0.03 asserted 1.00
s1 When seen as a function of the frequency this invariant collection of tori is called the KAM curve of the system. background 0.99 0.08 0.03 asserted 1.00
s2 Restricted to analytic regularity, we obtain strong quasi-analyticity properties for these objects. contribution 0.57 0.82 0.12 asserted 1.00
s3 In particular, we prove that KAM curves completely characterize the underlying systems. result 0.99 0.95 0.82 asserted 1.00
s4 We also show some of the dynamical implications on systems whose KAM curves share certain common features. result 0.53 0.93 0.07 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Classical KAM theory guarantees the existence of a positive measure set of invariant tori for sufficiently smooth non-degenerate near-integrable systems. When seen as a function of the frequency this invariant collection of tori is called the KAM curve of the system. Restricted to analytic regularity, we obtain strong quasi-analyticity properties for these objects. In particular, we prove that KAM curves completely characterize the underlying systems. We also show some of the dynamical implications on systems whose KAM curves share certain common features.

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