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Gibbs measures for hyperbolic attractors defined by densities

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David Parmenter, Mark Pollicott

Dynamical Systems · Submitted 17 Apr 2022

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

The authors' main claim By modifying the density at each step appropriately we show that the resulting measure is a prescribed Gibbs measure.

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arXiv ID2204.07991 (version 1)
Pith ID6JZT27T3, Pith's permanent record of this paper and its review
CitationDavid Parmenter, Mark Pollicott. "Gibbs measures for hyperbolic attractors defined by densities." arXiv:2204.07991 (2022). https://pith.science/paper/6JZT27T3
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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 0.11 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.98 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this article we will describe a new construction for Gibbs measures for hyperbolic attractors generalizing the original construction of Sinai, Bowen and Ruelle of SRB measures. The classical construction of the SRB measure is based on pushing forward the normalized volume on a piece of unstable manifold. By modifying the density at each step appropriately we show that the resulting measure is a prescribed Gibbs measure. This contrasts with, and complements, the construction of Climenhaga-Pesin-Zelerowicz who replace the volume on the unstable manifold by a fixed reference measure. Moreover, the simplicity of our proof, which uses only explicit properties on the growth rate of unstable manifold and entropy estimates, has the additional advantage that it applies in more general settings.

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 article we will describe a new construction for Gibbs measures for hyperbolic attractors generalizing the original construction of Sinai, Bowen and Ruelle of SRB measures. contribution 1.00 0.86 0.44 asserted 0.98
s1 The classical construction of the SRB measure is based on pushing forward the normalized volume on a piece of unstable manifold. background 1.00 0.04 0.03 asserted 1.00
s2 By modifying the density at each step appropriately we show that the resulting measure is a prescribed Gibbs measure. method 0.43 0.94 0.58 asserted 1.00
s3 This contrasts with, and complements, the construction of Climenhaga-Pesin-Zelerowicz who replace the volume on the unstable manifold by a fixed reference measure. interpretation 0.46 0.16 0.07 asserted 1.00
s4 Moreover, the simplicity of our proof, which uses only explicit properties on the growth rate of unstable manifold and entropy estimates, has the additional advantage that it applies in more general settings. interpretation 0.70 0.86 0.12 asserted 0.98

What kind of paper the classifier reports this is: method or tool 0.65 · evidence from proof or derivation 1.00.

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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 this article we will describe a new construction for Gibbs measures for hyperbolic attractors generalizing the original construction of Sinai, Bowen and Ruelle of SRB measures. The classical construction of the SRB measure is based on pushing forward the normalized volume on a piece of unstable manifold. By modifying the density at each step appropriately we show that the resulting measure is a prescribed Gibbs measure. This contrasts with, and complements, the construction of Climenhaga-Pesin-Zelerowicz who replace the volume on the unstable manifold by a fixed reference measure. Moreover, the simplicity of our proof, which uses only explicit properties on the growth rate of unstable manifold and entropy estimates, has the additional advantage that it applies in more general settings.

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