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Fractalization of Torus Revisited as a Strange Nonchaotic Attractor

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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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Takashi Nishikawa, Kunihiko Kaneko (Univ. of Tokyo Komaba)

chao-dyn · Submitted 3 Jul 1996

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

The authors' main claim Existence of fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor, as well as the Fourier mode analysis.

how it is stated · asserted 1.00 read the record →

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arXiv IDchao-dyn/9606019 (version 1)
Pith ID5FQVORBJ, Pith's permanent record of this paper and its review
CitationKunihiko Kaneko (Univ. of Tokyo Komaba), Takashi Nishikawa. "Fractalization of Torus Revisited as a Strange Nonchaotic Attractor." arXiv:chao-dyn/9606019 (1996). https://pith.science/paper/5FQVORBJ
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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, 3,010 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Fractalization of torus and its transition to chaos in a quasi-periodically forced logistic map is re-investigated in relation with a strange nonchaotic attractor, with the aid of functional equation for the invariant curve. Existence of fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor, as well as the Fourier mode analysis. Mechanisms of the onset of fractal torus and the transition to chaos are studied in connection with the intermittency.

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 Fractalization of torus and its transition to chaos in a quasi-periodically forced logistic map is re-investigated in relation with a strange nonchaotic attractor, with the aid of functional equation for the invariant curve. contribution 0.95 0.83 0.18 asserted 0.88
s1 Existence of fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor, as well as the Fourier mode analysis. result 0.99 0.88 0.23 asserted 1.00
s2 Mechanisms of the onset of fractal torus and the transition to chaos are studied in connection with the intermittency. contribution 0.96 0.83 0.13 asserted 0.89

What kind of paper the classifier reports this is: simulation study 0.74 · evidence from simulation or computation 0.84.

What was examined, and what was not

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  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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

Fractalization of torus and its transition to chaos in a quasi-periodically forced logistic map is re-investigated in relation with a strange nonchaotic attractor, with the aid of functional equation for the invariant curve. Existence of fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor, as well as the Fourier mode analysis. Mechanisms of the onset of fractal torus and the transition to chaos are studied in connection with the intermittency.

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