Acta mathematica scientia,Series B ›› 2003, Vol. 23 ›› Issue (2): 201-.

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THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET

 HU Di-He   

  1. College of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Online:2003-04-07 Published:2003-04-07
  • Supported by:

    Received June 11, 2001; revised June 13, 2002. Supported by NNSF of China and the Foundation of Wuhan
    University

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Abstract:

The structure of any a.s. self-similar set
$K(\bar{\omega})$ generated by a class of random elements
$\{g^{(\bar{\omega})}_{n,\sigma }\}$ taking values in the space of
contractive operators is given and  the approximation of
 $K(\bar{\omega})$ by the fixed points $\{p^{(\bar{\omega})}_{n,\sigma }\}$
of $\{g^{(\bar{\omega})}_{n,\sigma }\}$ is obtained.
It is useful to generate the fractal in computer.

Key words: a.s. self-similar set, Hausdorff metric, fixed point, structure, approximation

CLC Number: 

  • 60G17
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