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Volterra's realization of the KM-system

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M. A. Agrotis, P. A. Damianou

Mathematical Physics · Submitted 5 Oct 2005

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

The authors' main claim We construct a symplectic realization of the KM-system and obtain the higher order Poisson tensors and commuting flows via the use of a recursion operator.

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arXiv IDmath-ph/0510017 (version 1)
Pith IDIQ2RDGL5, Pith's permanent record of this paper and its review
CitationM. A. Agrotis, P. A. Damianou. "Volterra's realization of the KM-system." arXiv:math-ph/0510017 (2005). https://pith.science/paper/IQ2RDGL5
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,858 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.08 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We construct a symplectic realization of the KM-system and obtain the higher order Poisson tensors and commuting flows via the use of a recursion operator. This is achieved by doubling the number of variables through Volterra's coordinate transformation. An application of Oevel's theorem yields master symmetries, invariants and deformation relations.

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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 construct a symplectic realization of the KM-system and obtain the higher order Poisson tensors and commuting flows via the use of a recursion operator. contribution 0.89 0.95 0.72 asserted 1.00
s1 This is achieved by doubling the number of variables through Volterra's coordinate transformation. method 1.00 0.82 0.08 asserted 1.00
s2 An application of Oevel's theorem yields master symmetries, invariants and deformation relations. result 0.77 0.76 0.18 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

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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 construct a symplectic realization of the KM-system and obtain the higher order Poisson tensors and commuting flows via the use of a recursion operator. This is achieved by doubling the number of variables through Volterra's coordinate transformation. An application of Oevel's theorem yields master symmetries, invariants and deformation relations.

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