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Bifurcation diagram of the generalized 4th Appelrot class

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Mikhail P. Kharlamov

Exactly Solvable and Integrable Systems · Submitted 20 Jun 2009

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

The authors' main claim For these integrals the bifurcation diagram is established and the admissible region for the corresponding constants is found.

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arXiv ID0906.3780 (version 1)
Pith IDGZZ67WYQ, Pith's permanent record of this paper and its review
CitationMikhail P. Kharlamov. "Bifurcation diagram of the generalized 4th Appelrot class." arXiv:0906.3780 (2009). https://pith.science/paper/GZZ67WYQ
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,777 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.30 · compares with prior results 0.33 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The article continues the author's publication in [Mech. Tverd. Tela, No. 34, 2004], in which the generalizations of the Appelrot classes of the Kowalevski top motions are found for the case of the double force field. We consider the analogue of the 4th Appelrot class. The trajectories of this family fill the surface which is four-dimensional in the neighborhood of its generic points. The complete system of two integrals is pointed out. For these integrals the bifurcation diagram is established and the admissible region for the corresponding constants is found.

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 The article continues the author's publication in [Mech. Tverd. background 0.99 0.20 0.02 asserted 0.60
s1 Tela, No. 34, 2004], in which the generalizations of the Appelrot classes of the Kowalevski top motions are found for the case of the double force field. background 1.00 0.47 0.06 asserted 0.99
s2 We consider the analogue of the 4th Appelrot class. contribution 0.98 0.65 0.08 asserted 0.84
s3 The trajectories of this family fill the surface which is four-dimensional in the neighborhood of its generic points. result 0.96 0.77 0.15 asserted 1.00
s4 The complete system of two integrals is pointed out. contribution 0.58 0.86 0.10 asserted 0.99
s5 For these integrals the bifurcation diagram is established and the admissible region for the corresponding constants is found. result 0.83 0.93 0.55 asserted 1.00

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

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  • P abstract
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  • 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

The article continues the author's publication in [Mech. Tverd. Tela, No. 34, 2004], in which the generalizations of the Appelrot classes of the Kowalevski top motions are found for the case of the double force field. We consider the analogue of the 4th Appelrot class. The trajectories of this family fill the surface which is four-dimensional in the neighborhood of its generic points. The complete system of two integrals is pointed out. For these integrals the bifurcation diagram is established and the admissible region for the corresponding constants is found.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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