About the Book
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 Benoit 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.
Table of Contents:
Separation conditions for iterated function systems with overlaps by Q.-R. Deng, K.-S. Lau, and S.-M. Ngai $k$-point configurations of discrete self-similar sets by D. Essouabri and B. Lichtin Fractal complex dimensions, Riemann hypothesis and invertibility of the spectral operator by H. Herichi and M. L. Lapidus Analysis and geometry of the measurable Riemannian structure on the Sierpinski gasket by N. Kajino A survey on Minkowski measurability of self-similar and self-conformal fractals in $\mathbb{R}^d$ by S. Kombrink Minkowski measurability and exact fractal tube formulas for $p$-adic self-similar strings by M. L. Lapidus, H. Hung, and M. van Frankenhuijsen Minkowski measurability results for self-similar tilings and fractals with monophase generators by M. L. Lapidus, E. P. J. Pearse, and S. Winter Multifractal analysis via scaling zeta functions and recursive structure of lattice strings by R. de Santiago, M. L. Lapidus, S. A. Roby, and J. A. Rock Box-counting fractal strings, zeta functions, and equivalent forms of Minkowski dimension by M. L. Lapidus, J. A. Rock, and D. Zubrinic Hausdorff dimension of the limit set of countable conformal iterated function systems with overlaps by E. Mihailescu and M. Urbanski Multifractal tubes: Multifractal zeta-functions, multifractal Steiner formulas and explicit formulas by L. Olsen Laplacians on Julia sets III: Cubic Julia sets and formal matings by C. Spicer, R. S. Strichartz, and E. Totari Lipschitz equivalence of self-similar sets: Algebraic and geometric properties by H. Rao, H.-J. Ruan, and Y. Wang Riemann zeros in arithmetic progression by M. van Frankenhuijsen Curvature measures of fractal sets by M. Zahle
About the Author :
David Carfi, University of Messina, Italy, USA
Michel L. Lapidus, University of California, Riverside, CA, USA
Erin P. J. Pearse, California Polytechnic State University, San Luis Obispo, CA, USA
Machiel van Frankenhuijsen, Utah Valley University, Orem, UT, USA
