Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied 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 601
ISBNs: 978-0-8218-9148-3 (print); 978-1-4704-1083-4 (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 various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry).
The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.
Graduate students and researchers interested in applications of fractal geometry.
Table of Contents
- Eric Akkermans – Statistical Mechanics and Quantum Fields on Fractals
- Vladimir Balan – Spectral Algebra of the Chernov and Bogoslovsky Finsler Metric Tensors
- Julien Barral, Arnaud Durand, Stéphane Jaffard and Stéphane Seuret – Local Multifractal Analysis
- Laurent E. Calvet and Adlai J. Fisher – Extreme Risk and Fractal Regularity in Finance
- David Carfì and Angela Ricciardello – An Algorithm for Dynamical Games with Fractal-Like Trajectories
- Marcel Filoche and Svitlana Mayboroda – The Landscape of Anderson Localization in a Disordered Medium
- Daniele Guido and Tommaso Isola – Zeta Functions for Infinite Graphs and Functional Equations
- Michael Hinz and Alexander Teplyaev – Vector Analysis on Fractals and Applications
- Naotaka Kajino – Non-Regularly Varying and Non-Periodic Oscillation of the On-Diagonal Heat Kernels on Self-Similar Fractals
- Tom Kennedy and Gregory F. Lawler – Lattice Effects in the Scaling Limit of the Two-Dimensional Self-Avoiding Walk
- Robert Kesler and Benjamin Steinhurst – The Casimir Effect on Laakso Spaces
- Nishu Lal and Michel L. Lapidus – The Decimation Method for Laplacians on Fractals: Spectra and Complex Dynamics
- Michel L. Lapidus and Robert G. Niemeyer – The Current State of Fractal Billiards
- Céline Lévy-Leduc and Murad S. Taqqu – Long-Range Dependence and the Rank of Decompositions
- Bing Li, Narn-Rueih Shieh and Yimin Xiao – Hitting Probabilities of the Random Covering Sets
- Yūki Naito, Mervan Pašić, Satoshi Tanaka and Darko Žubrinić – Fractal Oscillations Near the Domain Boundary of Radially Symmetric Solutions of $p$-Laplace Equations
- John R. Quinn – Applications of the Contraction Mapping Principle
- Daniele Schilirò – Economics and Psychology. Perfect Rationality versus Bounded Rationality