Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot

By Michel L. Lapidus, M. V. Frankenhuijsen. 2004

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Distribution of rational maps with a preperiodic critical point (2006, background): “As external rays do not land in general, we are led to work with fibers, originally introduced by Schleicher [Sch].”
Dynamic rays of bounded-type entire functions (2007, result): “We note finally that our results also apply to the setting of “random iteration” (see [Com04]).”
Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences (2011, unknown): “Corollary 1 There exist functions k0, k ∈ S(Rn) with suppk0, suppk ⊂ {x ∈ Rn : |x| 1} and Dβk̂(0) = 0 for all 0 ≤ |β| α2 such that for all f ∈ S ′(Rn) ∥∥k0(1, f )w0|Lp(·) ( R n )∥∥ + ∥∥k(2−j , f )wj | q(·)(Lp(·)) ∥∥ is an equivalent norm on Bwp(·),q(·)(Rn).”
Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[8] M.”
Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators (2010, background): “An important subclass of fractal sprays is formed by self-similar tilings, which appear naturally in connection with self-similar sets and are higher-dimensional generalizations of the (geometric) self-similar strings studied in [29,27,28]; see Section 5.”