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A tube formula for the Koch snowflake curve, with applications to complex dimensions | | Michel L. Lapidus
; Erin P. J. Pearse
; | | Date: |
9 Dec 2004 | | Subject: | Mathematical Physics; Dynamical Systems; Spectral Theory MSC-class: Primary 26A30, 28A12, 28A75, 28A80; Secondary 11K55, 26A27, 28A78, 28D20, 42A16 | math-ph math.DS math.MP math.SP | | Abstract: | A formula for the interior epsilon-neighborhood of the classical von Koch snowflake curve is computed in detail. This function of epsilon is shown to match quite closely with earlier predictions of what it should be, but is also much more precise. The resulting `tube formula’ is expressed in terms of the Fourier coefficients of a suitable nonlinear and periodic analogue of the standard Cantor staircase function and reflects the self-similarity of the Koch curve. As a consequence, the possible complex dimensions of the Koch snowflake are computed explicitly. | | Source: | arXiv, math-ph/0412029 | | Services: | Forum | Review | PDF | Favorites | |
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