A trio of maps: chaos on an ellipse, a shark’s fin, and Sluze’s pearls

M McCartney

doi:10.1080/0020739X.2024.2319120

A trio of maps: chaos on an ellipse, a shark’s fin, and Sluze’s pearls

M McCartney

Research output: Contribution to journal › Conference article › peer-review

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Abstract

Three one-dimensional maps are presented. The maps are analysed with a combination of Feigenbaum diagrams, the calculation of global Lyapunov exponents, and the evaluation of fixed points. It is shown that in certain cases period two orbits can be evaluated by careful observation of the form of the related pairs of equations.
A range of classroom exercises are provided to enable students to investigate the maps further.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	International Journal of Mathematical Education in Science and Technology
Early online date	26 Feb 2024
DOIs	https://doi.org/10.1080/0020739X.2024.2319120
Publication status	Published online - 26 Feb 2024

Bibliographical note

Publisher Copyright:
© 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

Keywords

discrete chaos
logistic map
Feigenbaum diagram

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1080/0020739X.2024.2319120

A trio of maps chaos on an ellipse a shark s fin and Sluze s pearlsFinal published version, 2.2 MBLicence: CC BY-NC-ND

Cite this

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N2 - Three one-dimensional maps are presented. The maps are analysed with a combination of Feigenbaum diagrams, the calculation of global Lyapunov exponents, and the evaluation of fixed points. It is shown that in certain cases period two orbits can be evaluated by careful observation of the form of the related pairs of equations.A range of classroom exercises are provided to enable students to investigate the maps further.

AB - Three one-dimensional maps are presented. The maps are analysed with a combination of Feigenbaum diagrams, the calculation of global Lyapunov exponents, and the evaluation of fixed points. It is shown that in certain cases period two orbits can be evaluated by careful observation of the form of the related pairs of equations.A range of classroom exercises are provided to enable students to investigate the maps further.

KW - discrete chaos

KW - logistic map

KW - Feigenbaum diagram

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JO - International Journal of Mathematical Education in Science and Technology

JF - International Journal of Mathematical Education in Science and Technology

ER -

A trio of maps: chaos on an ellipse, a shark’s fin, and Sluze’s pearls

Abstract

Bibliographical note

Keywords

UN SDGs

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