Measuring the strangeness of strange attractors

Grassberger, P., & Procaccia, I. (1983). Measuring the strangeness of strange attractors. Physica D: Nonlinear Phenomena, 9(1–2), 1-2.

Type

Journal article

Intellectual base

Primary research

Year

1983

Volume

9

Issue

1–2

Pages

1-2

ISSN

0167-2789

DOI

10.1016/0167-2789(83)90298-1

DOI registrant

Elsevier

Link

https://doi.org/10.1016/0167-2789(83)90298-1

Cited from

mathematics

Cited by

4 citations across 3 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Chaos
  • 6. Mixing and structure: despite apparent disorder, the attractor has a characteristic structure (often fractal, with non-integer Hausdorff dimension as Grassberger and Procaccia (1983) operationalized through the correlation dimension)

    This sourceIntroduces the correlation dimension as a computationally tractable measure of fractal attractor dimension and a diagnostic distinguishing low-dimensional chaos from high-dimensional noise.

Domain-specific

• Correlation Dimension
  • For finite data, the Grassberger–Procaccia estimator counts close pairs over a range of radii and estimates the slope of `log C_N(r)` against `log r` in a defensible scaling region.

    This sourceDevelops the estimator, scaling interpretation, and comparisons with other dimensions.

• Correlation integral
  • Its small-radius scaling estimates correlation dimension, but temporal dependence, finite samples, noise, embedding choices and edge effects require exclusion windows and a defensible scaling region.
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Verification

Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.

Does it back the claim? Not recorded. Neither this nor any other of the 4 citations of this work carries a recorded support check.

Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.

See how references were verified.

Links previously used in the corpus

Before the registry existed this work was also linked 2 other ways.

• https://verga.cpt.univ-mrs.fr/pdfs/Grassberger-1983fk.pdf ×1
• https://www.sciencedirect.com/science/article/pii/0167278983902981 ×1

Registry ID ref:e15f38aa833c · see in the full table