Pith. Sign in

RECORD

Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
M. Romero-Bastida, Diego Pazó, Juan M. López, Miguel A. Rodríguez

Chaotic Dynamics · Submitted 30 Aug 2010

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

The authors' main claim In contrast, backward LVs (obtained via Gram-Schmidt orthonormalizations) present approximately the same scaling exponent in all cases, suggesting it is an artificial exponent produced by the imposed orthogonality of these vectors.

how it is stated · hedged possibility 0.89 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1008.5186 (version 2)
Pith ID2VJBRWQZ, Pith's permanent record of this paper and its review
CitationDiego Paz\'o, Juan M. L\'opez, Miguel A. Rodr\'iguez, M. Romero-Bastida. "Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices." arXiv:1008.5186 (2010). https://pith.science/paper/2VJBRWQZ
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,725 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.89 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In this work we perform a detailed study of the scaling properties of Lyapunov vectors (LVs) for two different one-dimensional Hamiltonian lattices: the Fermi-Pasta-Ulam and $\Phi^4$ models. In this case, characteristic (also called covariant) LVs exhibit qualitative similarities with those of dissipative lattices but the scaling exponents are different and seemingly nonuniversal. In contrast, backward LVs (obtained via Gram-Schmidt orthonormalizations) present approximately the same scaling exponent in all cases, suggesting it is an artificial exponent produced by the imposed orthogonality of these vectors. We are able to compute characteristic LVs in large systems thanks to a `bit reversible' algorithm, which completely obviates computer memory limitations.

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 In this work we perform a detailed study of the scaling properties of Lyapunov vectors (LVs) for two different one-dimensional Hamiltonian lattices: the Fermi-Pasta-Ulam and $\Phi^4$ models. contribution 1.00 0.95 0.06 asserted 0.88
s1 In this case, characteristic (also called covariant) LVs exhibit qualitative similarities with those of dissipative lattices but the scaling exponents are different and seemingly nonuniversal. result 0.95 0.67 0.21 asserted 0.84
s2 In contrast, backward LVs (obtained via Gram-Schmidt orthonormalizations) present approximately the same scaling exponent in all cases, suggesting it is an artificial exponent produced by the imposed orthogonality of these vectors. result 0.55 0.81 0.33 hedged possibility 0.89
s3 We are able to compute characteristic LVs in large systems thanks to a `bit reversible' algorithm, which completely obviates computer memory limitations. method 0.98 0.93 0.05 asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.97 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • 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

In this work we perform a detailed study of the scaling properties of Lyapunov vectors (LVs) for two different one-dimensional Hamiltonian lattices: the Fermi-Pasta-Ulam and $\Phi^4$ models. In this case, characteristic (also called covariant) LVs exhibit qualitative similarities with those of dissipative lattices but the scaling exponents are different and seemingly nonuniversal. In contrast, backward LVs (obtained via Gram-Schmidt orthonormalizations) present approximately the same scaling exponent in all cases, suggesting it is an artificial exponent produced by the imposed orthogonality of these vectors. We are able to compute characteristic LVs in large systems thanks to a `bit reversible' algorithm, which completely obviates computer memory limitations.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.