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Templates and subtemplates of R\"ossler attractors from a bifurcation diagram

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Martin Rosalie

Chaotic Dynamics · Submitted 24 Feb 2016

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

The authors' main claim Our main result is that only one template describe the topological structure of height attractors.

how it is stated · asserted 1.00 read the record →

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arXiv ID1602.07473 (version 1)
Pith IDLRPS56D6, Pith's permanent record of this paper and its review
CitationMartin Rosalie. "Templates and subtemplates of R\"ossler attractors from a bifurcation diagram." arXiv:1602.07473 (2016). https://pith.science/paper/LRPS56D6
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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, 5,377 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.20 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We study the bifurcation diagram of the R\"ossler system. It displays the various dynamical regimes of the system (stable or chaotic) when a parameter is varied. We choose a diagram that exhibits coexisting attractors and banded chaos. We use the topological characterization method to study these attractors. Then, we details how the templates of these attractors are subtemplates of a unique template. Our main result is that only one template describe the topological structure of height attractors. This leads to a topological partition of the bifurcation diagram that gives the symbolic dynamic of all bifurcation diagram attractors with a unique template.

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 study the bifurcation diagram of the R\"ossler system. contribution 0.86 0.90 0.01 asserted 0.88
s1 It displays the various dynamical regimes of the system (stable or chaotic) when a parameter is varied. background 1.00 0.12 0.02 asserted 1.00
s2 We choose a diagram that exhibits coexisting attractors and banded chaos. method 0.67 0.88 0.02 asserted 0.93
s3 We use the topological characterization method to study these attractors. method 1.00 0.89 0.02 asserted 0.94
s4 Then, we details how the templates of these attractors are subtemplates of a unique template. result 0.63 0.89 0.13 asserted 0.98
s5 Our main result is that only one template describe the topological structure of height attractors. result 1.00 0.90 0.97 asserted 1.00
s6 This leads to a topological partition of the bifurcation diagram that gives the symbolic dynamic of all bifurcation diagram attractors with a unique template. interpretation 0.79 0.89 0.19 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.94 · evidence from simulation or computation 0.85.

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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

We study the bifurcation diagram of the R\"ossler system. It displays the various dynamical regimes of the system (stable or chaotic) when a parameter is varied. We choose a diagram that exhibits coexisting attractors and banded chaos. We use the topological characterization method to study these attractors. Then, we details how the templates of these attractors are subtemplates of a unique template. Our main result is that only one template describe the topological structure of height attractors. This leads to a topological partition of the bifurcation diagram that gives the symbolic dynamic of all bifurcation diagram attractors with a unique template.

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