Pith. Sign in

RECORD

Ergodic theory and visualization. II. Harmonic mesochronic plots visualize (quasi)periodic sets

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
Zoran Levnajić, Igor Mezić

Chaotic Dynamics · Submitted 15 Aug 2008

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

The authors' main claim Besides identifying all periodic sets, our method is useful in detecting chaotic phase space regions with a good precision.

how it is stated · asserted 0.98 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID0808.2182 (version 2)
Pith ID36OEM6EN, Pith's permanent record of this paper and its review
CitationIgor Mezi\'c, Zoran Levnaji\'c. "Ergodic theory and visualization. II. Harmonic mesochronic plots visualize (quasi)periodic sets." arXiv:0808.2182 (2008). https://pith.science/paper/36OEM6EN
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, 3,676 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.49 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets or arbitrary periodicity in the phase space. Besides identifying all periodic sets, our method is useful in detecting chaotic phase space regions with a good precision. The range of method's applicability is illustrated using well-known Chirikov standard map, while its full potential is presented by studying higher-dimensional measure-preserving systems, in particular Froeschl\'e map and extended standard map.

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 We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. contribution 1.00 0.85 0.12 asserted 1.00
s1 Our method employs the novel concept of harmonic time average [2], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets or arbitrary periodicity in the phase space. method 0.95 0.85 0.21 asserted 1.00
s2 Besides identifying all periodic sets, our method is useful in detecting chaotic phase space regions with a good precision. result 0.81 0.82 0.28 asserted 0.98
s3 The range of method's applicability is illustrated using well-known Chirikov standard map, while its full potential is presented by studying higher-dimensional measure-preserving systems, in particular Froeschl\'e map and extended standard map. contribution 0.64 0.86 0.12 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · 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

We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets or arbitrary periodicity in the phase space. Besides identifying all periodic sets, our method is useful in detecting chaotic phase space regions with a good precision. The range of method's applicability is illustrated using well-known Chirikov standard map, while its full potential is presented by studying higher-dimensional measure-preserving systems, in particular Froeschl\'e map and extended standard map.

Human review

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

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 · 1 sentence without a confident label

Uses its method or tool 1 paper
  • Using the ideas developed in [ref] , it is possible to define a kernel $k_α$ that acts on this data set.

    Diffusion maps for changing data · Parameterized difference equations · 0.95

What it cites · 5 sentences without a confident label

Builds on 1 paper
Uses the method or tool of 1 paper
Compares with 1 paper

Discussion

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