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Kneading Theory for Triangular Maps

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Diana A. Mendes (ISCTE-Lisbon), J. Sousa Ramos (IST-Lisbon)

Dynamical Systems · Submitted 7 Jan 2003

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

The authors' main claim A direct consequence of these results is the rigorous computation of the topological entropy of two-dimensional triangular maps.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0301054 (version 2)
Pith IDXRLFW4TD, Pith's permanent record of this paper and its review
CitationDiana A. Mendes (ISCTE-Lisbon), J. Sousa Ramos (IST-Lisbon). "Kneading Theory for Triangular Maps." arXiv:math/0301054 (2003). https://pith.science/paper/XRLFW4TD
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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, 4,170 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The main purpose of this paper is to present a kneading theory for two-dimensional triangular maps. This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map. We also define a Markov partition by rectangles for the phase space of these maps. A direct consequence of these results is the rigorous computation of the topological entropy of two-dimensional triangular maps. The connection between kneading theory and subshifts of finite type is shown by using a commutative diagram derived from the homological configurations associated to $m-$modal maps of the interval.

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 The main purpose of this paper is to present a kneading theory for two-dimensional triangular maps. contribution 0.99 0.69 0.17 asserted 0.94
s1 This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map. method 0.98 0.93 0.06 asserted 1.00
s2 We also define a Markov partition by rectangles for the phase space of these maps. method 0.65 0.93 0.04 asserted 1.00
s3 A direct consequence of these results is the rigorous computation of the topological entropy of two-dimensional triangular maps. result 0.97 0.84 0.32 asserted 1.00
s4 The connection between kneading theory and subshifts of finite type is shown by using a commutative diagram derived from the homological configurations associated to $m-$modal maps of the interval. contribution 0.40 0.85 0.08 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.67 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
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

The main purpose of this paper is to present a kneading theory for two-dimensional triangular maps. This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map. We also define a Markov partition by rectangles for the phase space of these maps. A direct consequence of these results is the rigorous computation of the topological entropy of two-dimensional triangular maps. The connection between kneading theory and subshifts of finite type is shown by using a commutative diagram derived from the homological configurations associated to $m-$modal maps of the interval.

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