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Lyapunov exponents and Kolmogorov-Sinai entropy for a high-dimensional convex billiard

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Thomas Papenbrock (Institute for Nuclear Theory, University of Washington, Seattle, USA)

chao-dyn · Submitted 6 Sep 1999

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

The authors' main claim This system exhibits truly high-dimensional chaos, and 2N-4 Lyapunov exponents are found to be positive.

how it is stated · asserted 1.00 read the record →

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arXiv IDchao-dyn/9909009 (version 1)
Pith IDG2ENOJ7V, Pith's permanent record of this paper and its review
CitationSeattle, Thomas Papenbrock (Institute for Nuclear Theory, University of Washington, USA). "Lyapunov exponents and Kolmogorov-Sinai entropy for a high-dimensional convex billiard." arXiv:chao-dyn/9909009 (1999). https://pith.science/paper/G2ENOJ7V
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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.92 · compares with prior results 0.05 · mentions code or data availability 0.02.

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

We compute the Lyapunov exponents and the Kolmogorov-Sinai (KS) entropy for a self-bound N-body system that is realized as a convex billiard. This system exhibits truly high-dimensional chaos, and 2N-4 Lyapunov exponents are found to be positive. The KS entropy increases linearly with the numbers of particles. We examine the chaos generating defocusing mechanism and investigate how high-dimensional chaos develops in this system with no dispersing elements.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We compute the Lyapunov exponents and the Kolmogorov-Sinai (KS) entropy for a self-bound N-body system that is realized as a convex billiard. contribution 1.00 0.96 0.20 asserted 1.00
s1 This system exhibits truly high-dimensional chaos, and 2N-4 Lyapunov exponents are found to be positive. result 0.99 0.95 0.41 asserted 1.00
s2 The KS entropy increases linearly with the numbers of particles. result 1.00 0.88 0.25 asserted 1.00
s3 We examine the chaos generating defocusing mechanism and investigate how high-dimensional chaos develops in this system with no dispersing elements. contribution 0.98 0.89 0.08 unclear 0.51

What kind of paper the classifier reports this is: simulation study 0.98 · evidence from simulation or computation 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 compute the Lyapunov exponents and the Kolmogorov-Sinai (KS) entropy for a self-bound N-body system that is realized as a convex billiard. This system exhibits truly high-dimensional chaos, and 2N-4 Lyapunov exponents are found to be positive. The KS entropy increases linearly with the numbers of particles. We examine the chaos generating defocusing mechanism and investigate how high-dimensional chaos develops in this system with no dispersing elements.

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