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arXiv · 1507.07461

Graph-Directed Sprays and Their Tube Volumes via Functional Equations

Derya Çelik·Şahin Koçak·Yunus Özdemir·A. Ersin Üreyen
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Abstract

The notion of sprays introduced by Lapidus and his co-workers has proved useful in the context of fractal tube formulas. In the present note, we propose a more general concept of sprays, where we allow several generators to make them more convenient for applications to graph-directed fractals. Using a simple functional equation satisfied by the volume of the inner $\varepsilon$-neighborhood of such a generalized spray, we establish a tube formula for them.

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Derya Çelik, Şahin Koçak, Yunus Özdemir, A. Ersin Üreyen. 2015-07-27. Graph-Directed Sprays and Their Tube Volumes via Functional Equations. https://arxiv.org/abs/1507.07461

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