Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics I: Fractals in Pure Mathematics
About this Title
David Carfì, University of Messina, Messina, Italy, Michel L. Lapidus, University of California, Riverside, Riverside, CA, Erin P. J. Pearse, California Polytechnic State University, San Luis Obispo, CA and Machiel van Frankenhuijsen, Utah Valley University, Orem, UT, Editors
Publication: Contemporary Mathematics
Publication Year 2013: Volume 600
ISBNs: 978-0-8218-9147-6 (print); 978-1-4704-1082-7 (online)
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.
Graduate students and researchers interested in fractal geometry and dynamical systems.
Table of Contents
- Qi-Rong Deng, Ka-Sing Lau and Sze-Man Ngai – Separation Conditions for Iterated Function Systems with Overlaps
- Driss Essouabri and Ben Lichtin – $k-$point Configurations of Discrete Self-Similar Sets
- Hafedh Herichi and Michel L. Lapidus – Fractal Complex Dimensions, Riemann Hypothesis and Invertibility of the Spectral Operator
- Naotaka Kajino – Analysis and Geometry of the Measurable Riemannian Structure on the Sierpiński Gasket
- Sabrina Kombrink – A Survey on Minkowski Measurability of Self-Similar and Self-Conformal Fractals in $\mathbb R^d$
- Michel L. Lapidus, Lũ’ Hùng and Machiel van Frankenhuijsen – Minkowski Measurability and Exact Fractal Tube Formulas for $p$-Adic Self-Similar Strings
- Michel L. Lapidus, Erin P. J. Pearse and Steffen Winter – Minkowski Measurability Results for Self-Similar Tilings and Fractals with Monophase Generators
- Rolando de Santiago, Michel L. Lapidus, Scott A. Roby and John A. Rock – Multifractal Analysis via Scaling Zeta Functions and Recursive Structure of Lattice Strings
- Michel L. Lapidus, John A. Rock and Darko Žubrinić – Box-Counting Fractal Strings, Zeta Functions, and Equivalent Forms of Minkowski Dimension
- Eugen Mihailescu and Mariusz Urbański – Hausdorff Dimension of the Limit Set of Countable Conformal Iterated Function Systems with Overlaps
- Lars Olsen – Multifractal Tubes: Multifractal Zeta-Functions, Multifractal Steiner Formulas and Explicit Formulas
- Calum Spicer, Robert S. Strichartz and Emad Totari – Laplacians on Julia Sets III: Cubic Julia Sets and Formal Matings
- Hui Rao, Huo-Jun Ruan and Yang Wang – Lipschitz Equivalence of Self-Similar Sets: Algebraic and Geometric Properties
- Machiel van Frankenhuijsen – Riemann Zeros in Arithmetic Progression
- Martina Zähle – Curvature Measures of Fractal Sets