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Hausdorff dimension of a class of three-interval exchange maps

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Davit Karagulyan

Dynamical Systems · Submitted 8 Jan 2017

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

The authors' main claim We further show, that the new parameter set has positive, but not full Hausdorff dimension.

how it is stated · asserted 1.00 read the record →

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arXiv ID1701.01984 (version 2)
Pith IDR37XKYLG, Pith's permanent record of this paper and its review
CitationDavit Karagulyan. "Hausdorff dimension of a class of three-interval exchange maps." arXiv:1701.01984 (2017). https://pith.science/paper/R37XKYLG
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,528 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.79 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.34 · compares with prior results 0.93 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In \cite{B} Bourgain proves that Sarnak's disjointness conjecture holds for a certain class of Three-interval exchange maps. In the present paper we slightly improve the Diophantine condition of Bourgain and estimate the constants in the proof. We further show, that the new parameter set has positive, but not full Hausdorff dimension. This, in particular, implies that the Lebesgue measure of this set is zero.

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 \cite{B} Bourgain proves that Sarnak's disjointness conjecture holds for a certain class of Three-interval exchange maps. background 1.00 0.02 0.04 asserted 1.00
s1 In the present paper we slightly improve the Diophantine condition of Bourgain and estimate the constants in the proof. contribution 1.00 0.93 0.10 asserted 1.00
s2 We further show, that the new parameter set has positive, but not full Hausdorff dimension. result 0.99 0.95 0.61 asserted 1.00
s3 This, in particular, implies that the Lebesgue measure of this set is zero. interpretation 0.96 0.78 0.19 asserted 1.00

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

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  • C citations
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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 \cite{B} Bourgain proves that Sarnak's disjointness conjecture holds for a certain class of Three-interval exchange maps. In the present paper we slightly improve the Diophantine condition of Bourgain and estimate the constants in the proof. We further show, that the new parameter set has positive, but not full Hausdorff dimension. This, in particular, implies that the Lebesgue measure of this set is zero.

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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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