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The Hausdorff Measure of a Class of Sierpinski Carpets

Author: XiongYaHan
Tutor: ZhouJi
School: Sichuan Normal University
Course: Basic mathematics
Keywords: Hausdorff measure Packing measure Hausdorff dimension Packing dimension Self-similar set Sierpinski carpet
CLC: O174.12
Type: Master's thesis
Year: 2005
Downloads: 86
Quote: 1
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Abstract


1980s by the Mandelbrot (BBMandelbrot) was founded to provide a study of fractal geometry irregular geometric objects ideas, methods and techniques. Since a large number of irregular geometric objects appear in different areas of the natural sciences , and it was found that the irregular geometry collection offers many natural phenomena are often a better description , in recent years , the emerging discipline of fractal geometry in mathematics, physics, chemistry , biology, engineering and other disciplines with great success , while the different disciplines has stimulated significant issues raised in the further development of fractal geometry . Fractal geometry the birth and development of the entire scientific development of great significance , as MFShlesinger pointed out: \a decade , following two topics that these trends can be reversed: the non-linear dynamics and fractal geometry . former involves the movement of non-linear equations to determine the general universal behavior , while the latter is the study of self-similar or self- affine object geometry and geometric dynamics , both of which have been applied to a series of profound cross disciplines . \Until now , people have developed some good calculation and estimation of fractal sets of dimension methods and techniques and there are many fractal sets of dimension has also been , for example, for meeting the open set condition for self-similar set , its Hausdorff dimension number and packing dimension equal to its similarity dimension ; in the text [ 1 ] , the authors identified through Figure recursive construction of a class of self-similar set of Hausdorff dimension of the subset . However, for even seemingly simple fractal set , calculate and estimate its Hausdorff measure is a very difficult thing . So far , only a small number of dimensions not larger than a self-similar set of Hausdorff measure the exact value is calculated out, for example, in [ 2 ] identified a third Cantor set of Hausdorff measure is 1 ; week for collar, Wu in paper [ 3 ] to get some dimension is one of the Sierpinski carpet Hausdorff measure of 2 1/2 ; Qucheng Qin Rao

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Real Analysis,Real Variable > Measure Theory
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