Constructive Approximation

, Volume 5, Issue 1, pp 89–98 | Cite as

An exact formula for the measure dimensions associated with a class of piecewise linear maps

  • J. S. Geronimo
  • D. P. Hardin


An exact formula for the various measure dimensions of attractors associated with contracting similitudes is given. An example is constructed showing that for more general affine maps the various measure dimensions are not always equal.

AMS classification

26A 28A 41A 44A 

Key words and phrases

Hausdorff dimension Lyapunov dimension Similitudes 


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Copyright information

© Springer-Verlag New York Inc 1989

Authors and Affiliations

  • J. S. Geronimo
    • 1
  • D. P. Hardin
    • 2
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Mathematics DepartmentVanderbilt UniversityNashvilleUSA

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