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Non-dense orbits on topological dynamical systems

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Cao Zhao, Jiao Yang, Xiaoyao Zhou

Dynamical Systems · Submitted 8 Oct 2024

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

The authors' main claim We consider the non-dense orbit set $E(z_0)$ and show that for any non-transitive point $z_0\in X$, this set $E(z_0)$ is empty or carries full topological pressure.

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arXiv ID2410.05640 (version 1)
Pith IDHYYGVQE4, Pith's permanent record of this paper and its review
CitationCao Zhao, Jiao Yang, Xiaoyao Zhou. "Non-dense orbits on topological dynamical systems." arXiv:2410.05640 (2024). https://pith.science/paper/HYYGVQE4
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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, 2,296 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.20 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Let $(X,d,T )$ be a topological dynamical system with the specification property. We consider the non-dense orbit set $E(z_0)$ and show that for any non-transitive point $z_0\in X$, this set $E(z_0)$ is empty or carries full topological pressure.

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 Let $(X,d,T )$ be a topological dynamical system with the specification property. background 0.99 0.08 0.02 asserted 0.61
s1 We consider the non-dense orbit set $E(z_0)$ and show that for any non-transitive point $z_0\in X$, this set $E(z_0)$ is empty or carries full topological pressure. result 0.97 0.94 0.93 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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  • references and citing sentences
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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

Let $(X,d,T )$ be a topological dynamical system with the specification property. We consider the non-dense orbit set $E(z_0)$ and show that for any non-transitive point $z_0\in X$, this set $E(z_0)$ is empty or carries full topological pressure.

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