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Lyapunov exponents from geodesic spread in configuration space

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Monica Cerruti-Sola (1), Roberto Franzosi (2, 3), Marco Pettini (1, 3, 4) ((1) Osservatorio Astrofisico di Arcetri, Firenze, Italy; (2) Dipartimento di Fisica
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Universita' di Firenze, Italy; (3) INFN, Sezione di Firenze, Italy; (4) INFM, UdR di Firenze, Italy)

chao-dyn · Submitted 15 Oct 1998

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

The authors' main claim Therefore the instability exponents obtained through the JLC equation are in perfect quantitative agreement with usual Lyapunov exponents.

how it is stated · asserted 1.00 read the record →

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arXiv IDchao-dyn/9810020 (version 1)
Pith IDH3FLJZJN, Pith's permanent record of this paper and its review
Citation3, 3), 4) ((1) Osservatorio Astrofisico di Arcetri, Firenze, Italy), Italy; (2) Dipartimento di Fisica, Italy; (3) INFN, Italy; (4) INFM, Marco Pettini (1, Monica Cerruti-Sola (1), Roberto Franzosi (2, Sezione di Firenze, UdR di Firenze, Universita' di Firenze. "Lyapunov exponents from geodesic spread in configuration space." arXiv:chao-dyn/9810020 (1998). https://pith.science/paper/H3FLJZJN
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,736 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.38 · human participants 0.01 · controlled comparison 0.13 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The exact form of the Jacobi -- Levi-Civita (JLC) equation for geodesic spread is here explicitly worked out at arbitrary dimension for the configuration space manifold M_E = {q in R^N | V(q) < E} of a standard Hamiltonian system, equipped with the Jacobi (or kinetic energy) metric g_J. As the Hamiltonian flow corresponds to a geodesic flow on (M_E,g_J), the JLC equation can be used to study the degree of instability of the Hamiltonian flow. It is found that the solutions of the JLC equation are closely resembling the solutions of the standard tangent dynamics equation which is used to compute Lyapunov exponents. Therefore the instability exponents obtained through the JLC equation are in perfect quantitative agreement with usual Lyapunov exponents. This work completes a previous investigation that was limited only to two-degrees of freedom systems.

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 exact form of the Jacobi -- Levi-Civita (JLC) equation for geodesic spread is here explicitly worked out at arbitrary dimension for the configuration space manifold M_E = {q in R^N | V(q) < E} of a standard Hamiltonian system, equipped with the Jacobi (or kinetic energy) metric g_J. As the Hamiltonian flow corresponds to a geodesic flow on (M_E,g_J), the JLC equation can be used to study the degree of instability of the Hamiltonian flow. contribution 0.90 0.92 0.07 asserted 1.00
s1 It is found that the solutions of the JLC equation are closely resembling the solutions of the standard tangent dynamics equation which is used to compute Lyapunov exponents. result 1.00 0.92 0.14 asserted 1.00
s2 Therefore the instability exponents obtained through the JLC equation are in perfect quantitative agreement with usual Lyapunov exponents. result 0.98 0.86 0.84 asserted 1.00
s3 This work completes a previous investigation that was limited only to two-degrees of freedom systems. gap 0.45 0.46 0.03 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 0.99.

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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

The exact form of the Jacobi -- Levi-Civita (JLC) equation for geodesic spread is here explicitly worked out at arbitrary dimension for the configuration space manifold M_E = {q in R^N | V(q) < E} of a standard Hamiltonian system, equipped with the Jacobi (or kinetic energy) metric g_J. As the Hamiltonian flow corresponds to a geodesic flow on (M_E,g_J), the JLC equation can be used to study the degree of instability of the Hamiltonian flow. It is found that the solutions of the JLC equation are closely resembling the solutions of the standard tangent dynamics equation which is used to compute Lyapunov exponents. Therefore the instability exponents obtained through the JLC equation are in perfect quantitative agreement with usual Lyapunov exponents. This work completes a previous investigation that was limited only to two-degrees of freedom systems.

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