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SYMMETRIC ITINERARY SETS: ALGORITHMS AND NONLINEAR EXAMPLES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 100 / Issue 1 / August 2019
- Published online by Cambridge University Press:
- 20 March 2019, pp. 109-118
- Print publication:
- August 2019
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- Article
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We describe how to approximate fractal transformations generated by a one-parameter family of dynamical systems
$W:[0,1]\rightarrow [0,1]$ constructed from a pair of monotone increasing diffeomorphisms 
$W_{i}$ such that 
$W_{i}^{-1}:[0,1]\rightarrow [0,1]$ for 
$i=0,1$. An algorithm is provided for determining the unique parameter value such that the closure of the symbolic attractor 
$\overline{\unicode[STIX]{x1D6FA}}$ is symmetrical. Several examples are given, one in which the 
$W_{i}$ are affine and two in which the 
$W_{i}$ are nonlinear. Applications to digital imaging are also discussed.
