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Covariant Lyapunov vectors

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Francesco Ginelli, Hugues Chate', Roberto Livi, Antonio Politi

Chaotic Dynamics · Submitted 17 Dec 2012

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

The authors' main claim We then present a detailed description of a "dynamical" algorithm to compute the CLVs and show that it generically converges exponentially in time.

how it is stated · asserted 1.00 read the record →

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arXiv ID1212.3961 (version 1)
Pith ID355XML4I, Pith's permanent record of this paper and its review
CitationAntonio Politi, Francesco Ginelli, Hugues Chate', Roberto Livi. "Covariant Lyapunov vectors." arXiv:1212.3961 (2012). https://pith.science/paper/355XML4I
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,296 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.94 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The recent years have witnessed a growing interest for covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets' theorem for the properties of the CLVs. We then present a detailed description of a "dynamical" algorithm to compute the CLVs and show that it generically converges exponentially in time. We also discuss its numerical performance and compare it with other algorithms presented in literature. We finally illustrate how CLVs can be used to quantify deviations from hyperbolicity with reference to a dissipative system (a chain of H\'enon maps) and a Hamiltonian model (a Fermi-Pasta-Ulam chain).

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 recent years have witnessed a growing interest for covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. background 1.00 0.04 0.04 asserted 1.00
s1 Here we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets' theorem for the properties of the CLVs. background 0.74 0.39 0.04 asserted 0.73
s2 We then present a detailed description of a "dynamical" algorithm to compute the CLVs and show that it generically converges exponentially in time. method 0.78 0.92 0.26 asserted 1.00
s3 We also discuss its numerical performance and compare it with other algorithms presented in literature. contribution 0.65 0.82 0.04 asserted 0.52
s4 We finally illustrate how CLVs can be used to quantify deviations from hyperbolicity with reference to a dissipative system (a chain of H\'enon maps) and a Hamiltonian model (a Fermi-Pasta-Ulam chain). contribution 0.86 0.86 0.25 asserted 0.98

What kind of paper the classifier reports this is: review 0.69 · evidence from simulation or computation 0.69.

What was examined, and what was not

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  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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 recent years have witnessed a growing interest for covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets' theorem for the properties of the CLVs. We then present a detailed description of a "dynamical" algorithm to compute the CLVs and show that it generically converges exponentially in time. We also discuss its numerical performance and compare it with other algorithms presented in literature. We finally illustrate how CLVs can be used to quantify deviations from hyperbolicity with reference to a dissipative system (a chain of H\'enon maps) and a Hamiltonian model (a Fermi-Pasta-Ulam chain).

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How the literature uses it

2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

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