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1 results

  • 9 - Further Examples: Attractors and Limit Sets

  • from Part Two - Examples
  • Jonathan M. Fraser, University of St Andrews, Scotland
  • Book:
    Assouad Dimension and Fractal Geometry
    Published online:
    13 October 2020
    Print publication:
    29 October 2020, pp 137-159

  • Summary

    In this chapter we collect together discussion of several further families of fractal set. In Section 9.1 we consider self-conformal sets, which are another special case of IFS attractor. In Section 9.2 we consider sets invariant under parabolic interval maps. While these sets are similar in spirit to IFS attractors, they are not necessarily attractors of IFSs since the inverse branches of the associated dynamical system fail to be strict contractions. The resulting parabolic behaviour greatly influences the Assouad dimension of such sets. In Section 9.3 we consider limit sets of Kleinian groups which are invariant sets for the group action on the boundary of hyperbolic space.In Section 9.4 we consider the random limit sets resulting from Mandelbrot percolation.