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Some Symmetric Orbits for N-body Type Difference Equations

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Leshun Xu, Yong Li, Menglong Su

Dynamical Systems · Submitted 28 Dec 2006

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

The authors' main claim To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type difference equations, the variational approach and the method of minimizing the Lagrangian action are adopted and the strong force condition is considered correspondingly, which is an efficient method in studying those with singular potentials.

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arXiv IDmath/0612826 (version 1)
Pith IDQCACDPKL, Pith's permanent record of this paper and its review
CitationLeshun Xu, Menglong Su, Yong Li. "Some Symmetric Orbits for N-body Type Difference Equations." arXiv:math/0612826 (2006). https://pith.science/paper/QCACDPKL
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,971 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.10 · mentions code or data availability 0.02.

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

This paper introduces a new difference scheme to the difference equations for N-body type problems. To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type difference equations, the variational approach and the method of minimizing the Lagrangian action are adopted and the strong force condition is considered correspondingly, which is an efficient method in studying those with singular potentials. And the difference equation can also be taken into consideration of other periodic solutions with symmetric or choreographic constraint in further studies.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper introduces a new difference scheme to the difference equations for N-body type problems. contribution 0.99 0.93 0.10 asserted 1.00
s1 To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type difference equations, the variational approach and the method of minimizing the Lagrangian action are adopted and the strong force condition is considered correspondingly, which is an efficient method in studying those with singular potentials. method 0.93 0.70 0.26 asserted 1.00
s2 And the difference equation can also be taken into consideration of other periodic solutions with symmetric or choreographic constraint in further studies. future work 1.00 0.09 0.08 hedged possibility 0.97

What kind of paper the classifier reports this is: method or tool 0.98 · evidence from proof or derivation 0.98.

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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

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Original abstract

This paper introduces a new difference scheme to the difference equations for N-body type problems. To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type difference equations, the variational approach and the method of minimizing the Lagrangian action are adopted and the strong force condition is considered correspondingly, which is an efficient method in studying those with singular potentials. And the difference equation can also be taken into consideration of other periodic solutions with symmetric or choreographic constraint in further studies.

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