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Efficient algorithm for detecting unstable periodic orbits in chaotic systems

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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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Ruslan L. Davidchack, Ying-Cheng Lai

chao-dyn · Submitted 3 Jun 1999

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

The authors' main claim We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems.

how it is stated · asserted 1.00 read the record →

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arXiv IDchao-dyn/9906007 (version 1)
Pith IDXODT6EIW, Pith's permanent record of this paper and its review
CitationRuslan L. Davidchack, Ying-Cheng Lai. "Efficient algorithm for detecting unstable periodic orbits in chaotic systems." arXiv:chao-dyn/9906007 (1999). https://pith.science/paper/XODT6EIW
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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, 3,535 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of a new iterative scheme and an effective technique for selecting initial points. The iterative scheme is based on the semi-implicit Euler method, which has both fast and global convergence, and only a small number of initial points is sufficient to detect all unstable periodic orbits of a given period. The power of our method is illustrated by numerical examples of both two- and four-dimensional maps.

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 present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. contribution 1.00 0.92 0.76 asserted 1.00
s1 Our method consists of a new iterative scheme and an effective technique for selecting initial points. method 0.85 0.91 0.07 asserted 1.00
s2 The iterative scheme is based on the semi-implicit Euler method, which has both fast and global convergence, and only a small number of initial points is sufficient to detect all unstable periodic orbits of a given period. method 1.00 0.84 0.29 asserted 1.00
s3 The power of our method is illustrated by numerical examples of both two- and four-dimensional maps. result 0.72 0.91 0.08 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 1.00.

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • 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 present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of a new iterative scheme and an effective technique for selecting initial points. The iterative scheme is based on the semi-implicit Euler method, which has both fast and global convergence, and only a small number of initial points is sufficient to detect all unstable periodic orbits of a given period. The power of our method is illustrated by numerical examples of both two- and four-dimensional maps.

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