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Interiors of sets of vector fields with shadowing corresponding to certain classes of reparameterizations

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Sergey Tikhomirov

Dynamical Systems · Submitted 13 Oct 2010

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

The authors' main claim For the case of Lipschitz shadowing property the $C^1$-interior equals the set of structurally stable vector fields.

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arXiv ID1010.2768 (version 1)
Pith IDKLQ5CTFJ, Pith's permanent record of this paper and its review
CitationSergey Tikhomirov. "Interiors of sets of vector fields with shadowing corresponding to certain classes of reparameterizations." arXiv:1010.2768 (2010). https://pith.science/paper/KLQ5CTFJ
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,899 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.66 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.34 · compares with prior results 0.13 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We study $C^1$-interiors of sets of vector fields with various shadowing properties. For the case of Lipschitz shadowing property the $C^1$-interior equals the set of structurally stable vector fields. If the dimension of the manifold does not exceed 3 a similar result holds for the oriented shadowing property.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study $C^1$-interiors of sets of vector fields with various shadowing properties. contribution 0.97 0.88 0.07 unclear 0.52
s1 For the case of Lipschitz shadowing property the $C^1$-interior equals the set of structurally stable vector fields. result 1.00 0.76 0.43 asserted 1.00
s2 If the dimension of the manifold does not exceed 3 a similar result holds for the oriented shadowing property. result 0.98 0.72 0.13 asserted 0.99

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

What was examined, and what was not

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  • references and citing sentences
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  • C citations
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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

We study $C^1$-interiors of sets of vector fields with various shadowing properties. For the case of Lipschitz shadowing property the $C^1$-interior equals the set of structurally stable vector fields. If the dimension of the manifold does not exceed 3 a similar result holds for the oriented shadowing property.

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