Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics I: Fractals in Pure Mathematics

This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance. Readership Graduate students and researchers interested in fractal geometry and dynamical systems. Table of Contents Q.-R. Deng, K.-S. Lau, and S.-M. Ngai -- Separation conditions for iterated function systems with overlaps D. Essouabri and B. Lichtin -- k-point configurations of discrete self-similar sets H. Herichi and M. L. Lapidus -- Fractal complex dimensions, Riemann hypothesis and invertibility of the spectral operator N. Kajino -- Analysis and geometry of the measurable Riemannian structure on the Sierpiński gasket S. Kombrink -- A survey on Minkowski measurability of self-similar and self-conformal fractals in Rd M. L. Lapidus, L. Hùng, and M. van Frankenhuijsen -- Minkowski measurability and exact fractal tube formulas for p-adic self-similar strings M. L. Lapidus, E. P. J. Pearse, and S. Winter -- Minkowski measurability results for self-similar tilings and fractals with monophase generators R. de Santiago, M. L. Lapidus, S. A. Roby, and J. A. Rock -- Multifractal analysis via scaling zeta functions and recursive structure of lattice strings M. L. Lapidus, J. A. Rock, and D. Žubrinić -- Box-counting fractal strings, zeta functions, and equivalent forms of Minkowski dimension E. Mihailescu and M. Urbański -- Hausdorff dimension of the limit set of countable conformal iterated function systems with overlaps L. Olsen -- Multifractal tubes: Multifractal zeta-functions, multifractal Steiner formulas and explicit formulas C. Spicer, R. S. Strichartz, and E. Totari -- Laplacians on Julia sets III: Cubic Julia sets and formal matings H. Rao, H.-J. Ruan, and Y. Wang -- Lipschitz equivalence of self-similar sets: Algebraic and geometric properties M. van Frankenhuijsen -- Riemann zeros in arithmetic progression M. Zähle -- Curvature measures of fractal sets