Quasi Harmonic Functions On Finite-Type Fractals

Quasi-Harmonic Functions on Finite oddball Fractals Nguyen Viet Hung Mathias Mesing Department of Mathematics and training processing system Science University of Greifswald, Germany Workshop Fractal abstract 2005 - 09 - 15  conception Fractals of ?nite vitrine Constructing algorithmic dramatic playctions showcase Outline 1 Introduction Fractals of ?nite type Constructing recursive functions Example 2 3 4 Hung, Mesing (Greifswald) analysis on Finite Type Fractals Fractal outline 2005 2 / 23 Introduction Fractals of ?nite type Constructing recursive functions Example Notations let fi : Rd ? Rd contractions with same ratio r , i ? S = {1, . . . , m}, and E the belonging unceasing set. Set S n := {(ui )i=1,...,n | ui ? S ? i = 1, . . . , n}, S ? := n?N S n . For u := u1 . . . un ? S ? de?ne fu := fu1 ? . . . ? fun and Eu := fu (E ). Example (Christmas channelize fractal) fi : C ? C, i = 1, 2, 3 fi (z) = a (z + ci ) with ci = e a= 2?(i?1) 3 , 7 4 1/( 1 2 ? + +i 3 2 ) Hung, Mesing (Greifswald) analysis on Finite Type Fractals Fractal Analysis 2005 3 / 23 Introduction Fractals of ?nite type Constructing recursive functions Example Motivation Harmonic functions on Sierpinski gasket visualize functions on points of E . envision the values at new points by averaging rules: g (x) = g (y ) = g (z) = g (a)+2g (b)+2g (c) 5 2g (a)+g (b)+2g (c) 5 2g (a)+2g (b)+g (c) 5 New approach Regard functions on subpieces of E . Use averaging rules to calculate the values on smaller pieces. Hung, Mesing (Greifswald) Analysis on Finite Type Fractals Fractal Analysis 2005 4 / 23 Introduction Fractals of ?nite type Constructing recursive functions Example Motivation Harmonic functions on Sierpinski gasket Regard functions on points of E . Calculate the values at new points by averaging rules: g (x) = g (y ) = g (z) = g (a)+2g (b)+2 g (c) 5 2g (a)+g (b)+2g (c) 5 2g (a)+2g (b)+! g (c) 5...If you want to get a full essay, bless it on our website: OrderCustomPaper.com

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