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Symmetric itinerary sets: Algorithms and nonlinear examples

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posted on 2021-10-31, 19:56 authored by Thomas HardingThomas Harding
We describe how to approximate fractal transformations generated by a one-parameter family of dynamical systems W: [0, 1] → [0, 1] constructed from a pair of monotone increasing diffeomorphisms Wi such that W-1i : [0, 1] → [0, 1] for → = 0, 1. An algorithm is provided for determining the unique parameter value such that the closure of the symbolic attractor is symmetrical. Several examples are given, one in which the Wi are affine and two in which the Wi are nonlinear. Applications to digital imaging are also discussed.

History

Preferred citation

Harding, B. (2019). Symmetric itinerary sets: Algorithms and nonlinear examples. Bulletin of the Australian Mathematical Society, 100(1), 109-118. https://doi.org/10.1017/S0004972719000297

Journal title

Bulletin of the Australian Mathematical Society

Volume

100

Issue

1

Publication date

2019-08-01

Pagination

109-118

Publisher

Cambridge University Press (CUP)

Publication status

Published

Online publication date

2019-03-20

ISSN

0004-9727

eISSN

1755-1633

Language

en

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