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Article: Sub-self-conformal sets.(Report)
- Article from:
- Scientia Magna
- Article date:
- December 1, 2007
- Author:
CopyrightCOPYRIGHT 2007 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Abstract The definition of sub-self-conformal set is given, and we obtain the formula for their Hausdorff and box dimension.
Keywords Sub-self-conformal set, symbolic space, Hausdorff dimension, box dimension.
[section]1. Introduction
Self-similar sets presented by Hutchinson [1] have been extensively studied. See for example [2] [3] [5] [8]. Let's recall that. Let X [subset or equal to] [R.sup.n] be a nonempty compact set, and there exists 0
[absolute value of w(x) - w(y)][less than or equal to C[absolute value of x - y], [for all]x, y [member of] X.
Then we say that w : X [right arrow] X is a contractive map. If each [w.sub.i](1 [less ...