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Hausdorff limits of external rays: the topological picture

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Carsten Lunde Petersen, Saeed Zakeri

Dynamical Systems · Submitted 2 Sep 2023

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

The authors' main claim We study Hausdorff limits of the external rays of a given periodic angle along a convergent sequence of polynomials of degree $d \geq 2$ with connected Julia sets.

how it is stated · asserted 0.75 read the record →

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arXiv ID2309.01027 (version 2)
Pith IDYMQ6V56Q, Pith's permanent record of this paper and its review
CitationCarsten Lunde Petersen, Saeed Zakeri. "Hausdorff limits of external rays: the topological picture." arXiv:2309.01027 (2023). https://pith.science/paper/YMQ6V56Q
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,634 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We study Hausdorff limits of the external rays of a given periodic angle along a convergent sequence of polynomials of degree $d \geq 2$ with connected Julia sets.

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 study Hausdorff limits of the external rays of a given periodic angle along a convergent sequence of polynomials of degree $d \geq 2$ with connected Julia sets. contribution 1.00 0.86 0.11 asserted 0.75

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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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 study Hausdorff limits of the external rays of a given periodic angle along a convergent sequence of polynomials of degree $d \geq 2$ with connected Julia sets.

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References
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1 arXiv paper cite this in 1 sentence

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

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