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A relation between entropy and transitivity of Anosov diffeomorphisms

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F. Micena

Dynamical Systems · Submitted 16 Mar 2022

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

The authors' main claim Under suitable hypothesis on Lyapunov exponents on the set of periodic points and the structure of the MME we get transitivity of $C^1-$Anosov diffeomorphisms.

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arXiv ID2203.08934 (version 1)
Pith IDVSMR5TRI, Pith's permanent record of this paper and its review
CitationF. Micena. "A relation between entropy and transitivity of Anosov diffeomorphisms." arXiv:2203.08934 (2022). https://pith.science/paper/VSMR5TRI
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,885 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.63 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.63 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

It is known that transitive Anosov diffeomorphisms have a unique measure of maximal entropy (MME). Here we discuss the converse question. Under suitable hypothesis on Lyapunov exponents on the set of periodic points and the structure of the MME we get transitivity of $C^1-$Anosov diffeomorphisms.

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 It is known that transitive Anosov diffeomorphisms have a unique measure of maximal entropy (MME). background 1.00 0.03 0.04 asserted 1.00
s1 Here we discuss the converse question. gap 0.47 0.44 0.03 unclear 0.89
s2 Under suitable hypothesis on Lyapunov exponents on the set of periodic points and the structure of the MME we get transitivity of $C^1-$Anosov diffeomorphisms. result 0.90 0.86 0.91 asserted 0.92

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.96.

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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

It is known that transitive Anosov diffeomorphisms have a unique measure of maximal entropy (MME). Here we discuss the converse question. Under suitable hypothesis on Lyapunov exponents on the set of periodic points and the structure of the MME we get transitivity of $C^1-$Anosov diffeomorphisms.

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