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Group automorphisms with few and with many periodic points

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Thomas Ward

Dynamical Systems · Submitted 19 Jun 2003

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

The authors' main claim For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C.

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arXiv IDmath/0306292 (version 1)
Pith IDAR7YETNC, Pith's permanent record of this paper and its review
CitationThomas Ward. "Group automorphisms with few and with many periodic points." arXiv:math/0306292 (2003). https://pith.science/paper/AR7YETNC
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The compiled record

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, 2,378 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.42 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.75 · compares with prior results 0.35 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C. $$ This may be interpreted as a combinatorial analogue of the (still open) problem of whether compact group automorphisms exist with any given topological entropy.

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 For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C. result 0.73 0.93 0.88 asserted 1.00
s1 $$ This may be interpreted as a combinatorial analogue of the (still open) problem of whether compact group automorphisms exist with any given topological entropy. interpretation 1.00 0.12 0.08 hedged possibility 1.00

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

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • 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

For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C. $$ This may be interpreted as a combinatorial analogue of the (still open) problem of whether compact group automorphisms exist with any given topological entropy.

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