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SYMMETRIC ITINERARY SETS: ALGORITHMS AND NONLINEAR EXAMPLES

  • BRENDAN HARDING (a1)

Abstract

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.

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The author acknowledges support from an Australian Research Council Discovery Project (project number DP160102021) funded by the Australian Government.

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SYMMETRIC ITINERARY SETS: ALGORITHMS AND NONLINEAR EXAMPLES

  • BRENDAN HARDING (a1)

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