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Shadowing near nonhyperbolic fixed points

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Alexey A. Petrov, Sergei Yu. Pilyugin

Dynamical Systems · Submitted 1 Oct 2013

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

The authors' main claim We use Lyapunov type functions to find conditions of finite shadowing in a neighborhood of a nonhyperbolic fixed point of a one-dimensional or two-dimensional homeomorphism or diffeomorphism.

how it is stated · asserted 1.00 read the record →

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arXiv ID1310.0496 (version 2)
Pith IDC4JQTFQF, Pith's permanent record of this paper and its review
CitationAlexey A. Petrov, Sergei Yu. Pilyugin. "Shadowing near nonhyperbolic fixed points." arXiv:1310.0496 (2013). https://pith.science/paper/C4JQTFQF
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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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,306 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.17 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We use Lyapunov type functions to find conditions of finite shadowing in a neighborhood of a nonhyperbolic fixed point of a one-dimensional or two-dimensional homeomorphism or diffeomorphism. A new concept of shadowing in which we control the size of one-step errors is introduced in the case of a nonisolated fixed point.

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 use Lyapunov type functions to find conditions of finite shadowing in a neighborhood of a nonhyperbolic fixed point of a one-dimensional or two-dimensional homeomorphism or diffeomorphism. contribution 0.77 0.94 0.40 asserted 1.00
s1 A new concept of shadowing in which we control the size of one-step errors is introduced in the case of a nonisolated fixed point. contribution 1.00 0.89 0.21 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.89 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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 use Lyapunov type functions to find conditions of finite shadowing in a neighborhood of a nonhyperbolic fixed point of a one-dimensional or two-dimensional homeomorphism or diffeomorphism. A new concept of shadowing in which we control the size of one-step errors is introduced in the case of a nonisolated fixed point.

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