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On the Myrberg Limit Sets and Bowen-Margulis-Sullivan Measures for Visibility Manifolds without Conjugate Points

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Fei Liu

Dynamical Systems · Submitted 1 Jul 2024

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

The authors' main claim We prove that the positivity of the Patterson-Sullivan measure of the Myrberg limit set is equivalent to the conservativity of the geodesic flow with respect to the Bowen-Margulis-Sullivan measure.

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arXiv ID2407.00910 (version 3)
Pith ID2HJLSUXD, Pith's permanent record of this paper and its review
CitationFei Liu. "On the Myrberg Limit Sets and Bowen-Margulis-Sullivan Measures for Visibility Manifolds without Conjugate Points." arXiv:2407.00910 (2024). https://pith.science/paper/2HJLSUXD
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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, 4,262 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.85 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

In this paper, we clarify the strong relationship between Myrberg type dynamics and the ergodic properties of the geodesic flows on (not necessarily compact) uniform visibility manifolds without conjugate points. We prove that the positivity of the Patterson-Sullivan measure of the Myrberg limit set is equivalent to the conservativity of the geodesic flow with respect to the Bowen-Margulis-Sullivan measure. Moreover we show that the Myrberg limit set is a full Patterson-Sullivan measure subset of the conical limit set. These results extend the classical works of P. Tukia and B. Stratmann from hyperbolic manifolds to the manifolds without conjugate points.

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 paper, we clarify the strong relationship between Myrberg type dynamics and the ergodic properties of the geodesic flows on (not necessarily compact) uniform visibility manifolds without conjugate points. contribution 0.96 0.75 0.26 asserted 0.98
s1 We prove that the positivity of the Patterson-Sullivan measure of the Myrberg limit set is equivalent to the conservativity of the geodesic flow with respect to the Bowen-Margulis-Sullivan measure. result 1.00 0.94 0.61 asserted 1.00
s2 Moreover we show that the Myrberg limit set is a full Patterson-Sullivan measure subset of the conical limit set. result 1.00 0.94 0.22 asserted 1.00
s3 These results extend the classical works of P. Tukia and B. background 0.37 0.15 0.03 asserted 0.79
s4 Stratmann from hyperbolic manifolds to the manifolds without conjugate points. contribution 0.52 0.23 0.04 asserted 0.71

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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  • references and citing sentences
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  • P abstract
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  • 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 paper, we clarify the strong relationship between Myrberg type dynamics and the ergodic properties of the geodesic flows on (not necessarily compact) uniform visibility manifolds without conjugate points. We prove that the positivity of the Patterson-Sullivan measure of the Myrberg limit set is equivalent to the conservativity of the geodesic flow with respect to the Bowen-Margulis-Sullivan measure. Moreover we show that the Myrberg limit set is a full Patterson-Sullivan measure subset of the conical limit set. These results extend the classical works of P. Tukia and B. Stratmann from hyperbolic manifolds to the manifolds without conjugate points.

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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

What it cites · 5 sentences without a confident label

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Cites as background 4 papers

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