Self-Affine Vector Measures and Vector Calculus on Fractals

  • F. Mendivil
  • E. R. Vrscay
Conference paper
Part of the The IMA Volumes in Mathematics and its Application book series (IMA, volume 132)


In this paper, we construct an IFS framework for studying self-similar vector measures. These measures have several applications, including the tangent and normal vector measure “fields” to fractal curves. Using the tangent vector measure, we define a line integral of a smooth vector field over a fractal curve. This then leads to a formulation of Green’s Theorem (and the Divergence Theorem) for planar regions bounded by fractal curves. The general IFS setting also leads to “probability measure” — valued measures, which give one way to coloring the geometric attractor of an IFS in a self-similar way.


Vector Measure Iterate Function System Borel Probability Measure Fractal Curve Markov Operator 


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Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • F. Mendivil
    • 1
  • E. R. Vrscay
    • 2
  1. 1.Department of Mathematics and StatisticsAcadia UniversityWolfvilleCanada
  2. 2.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

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