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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)

Abstract

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.

Keywords

Vector Measure Iterate Function System Borel Probability Measure Fractal Curve Markov Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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