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Existence and stability of Camm type steady states in galactic dynamics

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Yan Guo, Gerhard Rein

Mathematical Physics · Submitted 15 Mar 1999

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

The authors' main claim We prove the existence and nonlinear stability of Camm type steady states of the Vlasov-Poisson system in the gravitational case.

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arXiv IDmath-ph/9903032 (version 1)
Pith IDBCEHAH6H, Pith's permanent record of this paper and its review
CitationGerhard Rein, Yan Guo. "Existence and stability of Camm type steady states in galactic dynamics." arXiv:math-ph/9903032 (1999). https://pith.science/paper/BCEHAH6H
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,341 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.43 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We prove the existence and nonlinear stability of Camm type steady states of the Vlasov-Poisson system in the gravitational case. The paper demonstrates the effectiveness of an approach to the existence and stability problem for steady states, which was used in previous work by the authors: The steady states are obtained as minimizers of an energy-Casimir functional, and from this fact their dynamical stability is deduced.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We prove the existence and nonlinear stability of Camm type steady states of the Vlasov-Poisson system in the gravitational case. result 0.86 0.96 0.93 asserted 1.00
s1 The paper demonstrates the effectiveness of an approach to the existence and stability problem for steady states, which was used in previous work by the authors: The steady states are obtained as minimizers of an energy-Casimir functional, and from this fact their dynamical stability is deduced. method 0.94 0.63 0.13 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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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 prove the existence and nonlinear stability of Camm type steady states of the Vlasov-Poisson system in the gravitational case. The paper demonstrates the effectiveness of an approach to the existence and stability problem for steady states, which was used in previous work by the authors: The steady states are obtained as minimizers of an energy-Casimir functional, and from this fact their dynamical stability is deduced.

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