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Critical Attractor and Universality in a Renormalization Scheme for Three Frequency Hamiltonian Systems

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C. Chandre, H.R. Jauslin

chao-dyn · Submitted 2 Jul 1998

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

The authors' main claim We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor.

how it is stated · asserted 1.00 read the record →

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arXiv IDchao-dyn/9807007 (version 2)
Pith ID54IXMGZC, Pith's permanent record of this paper and its review
CitationC. Chandre, H.R. Jauslin. "Critical Attractor and Universality in a Renormalization Scheme for Three Frequency Hamiltonian Systems." arXiv:chao-dyn/9807007 (1998). https://pith.science/paper/54IXMGZC
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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, 3,503 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.23 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for three degrees of freedom Hamiltonian systems. The scheme is implemented for the spiral mean torus. We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor. We compute scaling exponents associated with this fixed set, and find that they can be expected to be universal.

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 an approximate renormalization-group transformation to analyze the breakup of invariant tori for three degrees of freedom Hamiltonian systems. contribution 0.94 0.91 0.06 asserted 0.83
s1 The scheme is implemented for the spiral mean torus. method 0.79 0.87 0.03 asserted 1.00
s2 We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor. result 1.00 0.96 0.57 asserted 1.00
s3 We compute scaling exponents associated with this fixed set, and find that they can be expected to be universal. result 0.50 0.93 0.41 hedged possibility 0.81

What kind of paper the classifier reports this is: simulation study 0.89 · evidence from simulation or computation 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 study an approximate renormalization-group transformation to analyze the breakup of invariant tori for three degrees of freedom Hamiltonian systems. The scheme is implemented for the spiral mean torus. We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor. We compute scaling exponents associated with this fixed set, and find that they can be expected to be universal.

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