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Nonstandard Smooth Realizations of Liouville Rotations

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Bassam Fayad, Maria Saprykina, Alistair Windsor

Dynamical Systems · Submitted 14 Aug 2006

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

The authors' main claim This allows us to construct ergodic volume preserving diffeomorphisms measure-theoretically isomorphic to any apriori given Liouville rotation on a variety of manifolds.

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arXiv IDmath/0608322 (version 1)
Pith IDAFMMISSW, Pith's permanent record of this paper and its review
CitationAlistair Windsor, Bassam Fayad, Maria Saprykina. "Nonstandard Smooth Realizations of Liouville Rotations." arXiv:math/0608322 (2006). https://pith.science/paper/AFMMISSW
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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, 2,903 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.46 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We augment the method of $C^\infty$ conjugation approximation with explicit estimates on the conjugacy map. This allows us to construct ergodic volume preserving diffeomorphisms measure-theoretically isomorphic to any apriori given Liouville rotation on a variety of manifolds. In the special case of tori the maps can be made uniquely ergodic.

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 We augment the method of $C^\infty$ conjugation approximation with explicit estimates on the conjugacy map. method 0.59 0.90 0.07 asserted 1.00
s1 This allows us to construct ergodic volume preserving diffeomorphisms measure-theoretically isomorphic to any apriori given Liouville rotation on a variety of manifolds. result 0.83 0.93 0.78 asserted 0.99
s2 In the special case of tori the maps can be made uniquely ergodic. result 0.99 0.86 0.13 hedged possibility 0.59

What kind of paper the classifier reports this is: theoretical result 0.80 · evidence from proof or derivation 1.00.

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  • 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

We augment the method of $C^\infty$ conjugation approximation with explicit estimates on the conjugacy map. This allows us to construct ergodic volume preserving diffeomorphisms measure-theoretically isomorphic to any apriori given Liouville rotation on a variety of manifolds. In the special case of tori the maps can be made uniquely ergodic.

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