• Title/Summary/Keyword: $\sigma$-multifractal

Search Result 1, Processing Time 0.021 seconds

MEASURE DERIVATIVE AND ITS APPLICATIONS TO $\sigma$-MULTIFRACTALS

  • Kim, Tae-Sik;Ahn, Tae-Hoon;Kim, Gwang-Il
    • Journal of the Korean Mathematical Society
    • /
    • v.36 no.1
    • /
    • pp.229-241
    • /
    • 1999
  • The fractal space is often associated with natural phenomena with many length scales and the functions defined on this space are usually not differentiable. First we define a $\sigma$-multifractal from $\sigma$-iterated function systems with probability. We introduce the measure derivative through the invariant measure of the $\sigma$-multifractal. We show that the non-differentiable function on the $\sigma$-multifractal can be differentiable with respect to this measure derivative. We apply this result to some examples of ordinary differential equations and diffusion processes on $\sigma$-multifractal spaces.

  • PDF