**Contemporary Mathematics**

Volume: 601;
2013;
372 pp;
Softcover

MSC: Primary 28; 37; 58; 60; 81; 91;

**Print ISBN: 978-0-8218-9148-3
Product Code: CONM/601**

List Price: $123.00

AMS Member Price: $98.40

MAA Member Price: $110.70

**Electronic ISBN: 978-1-4704-1083-4
Product Code: CONM/601.E**

List Price: $123.00

AMS Member Price: $98.40

MAA Member Price: $110.70

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# Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics

Share this page *Edited by *
*David Carfì; Michel L. Lapidus; Erin P. J. Pearse; Machiel van Frankenhuijsen*

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.

#### Readership

Graduate students and researchers interested in applications of fractal geometry.

# Table of Contents

## Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics

- Preface vii8 free
- Statistical Mechanics and Quantum Fields on Fractals 110 free
- 1. Introduction 110
- 2. Discrete scaling symmetry - Self similarity - Definitions 211
- 3. Heat kernel and spectral functions - Generalities 615
- 4. Laplacian on fractals - Heat kernel and spectral zeta function 1120
- 5. Thermodynamics on photons : The fractal blackbody [34] 1423
- 6. Conclusion and some open questions 1726
- Acknowledgments 1827
- References 1827

- Spectral Algebra of the Chernov and Bogoslovsky Finsler Metric Tensors 2332
- Local Multifractal Analysis 3140
- 1. Introduction 3140
- 2. Properties of the local Hausdorff dimension and the local multifractal spectrum 3443
- 3. A local multifractal formalism for a dyadic family 3847
- 4. Measures with varying local spectrum 4453
- 5. Local spectrum of stochastic processes 4857
- 6. Other regularity exponents characterized by dyadic families 5564
- 7. A functional analysis point of view 5867
- Acknowledgement 6170
- References 6170

- Extreme Risk and Fractal Regularity in Finance 6574
- An Algorithm for Dynamical Games with Fractal-Like Trajectories 95104
- The Landscape of Anderson Localization in a Disordered Medium 113122
- Zeta Functions for Infinite Graphs and Functional Equations 123132
- Vector Analysis on Fractals and Applications 147156
- Non-Regularly Varying and Non-Periodic Oscillation of the On-Diagonal Heat Kernels on Self-Similar Fractals 165174
- Lattice Effects in the Scaling Limit of the Two-Dimensional Self-Avoiding Walk 195204
- The Casimir Effect on Laakso Spaces 211220
- The Decimation Method for Laplacians on Fractals: Spectra and Complex Dynamics 227236
- The Current State of Fractal Billiards 251260
- Long-Range Dependence and the Rank of Decompositions 289298
- 1. Introduction 289298
- 2. The Gaussian case 291300
- 3. The linear case: Surgailis approach 293302
- 4. The linear case: Ho and Hsing approach 295304
- 5. Application to the polynomial case 297306
- 6. Sketches of proofs of Theorems 2.2 , 3.2 and 4.2 299308
- 7. Conclusion 304313
- Acknowledgments 304313
- References 304313

- Hitting Probabilities of the Random Covering Sets 307316
- Fractal Oscillations Near the Domain Boundary of Radially Symmetric Solutions of 𝑝-Laplace Equations 325334
- Applications of the Contraction Mapping Principle 345354
- 1. The Contraction Mapping Principle 345354
- 2. Corollaries, Applications and Implications 347356
- 3. Fractal Method of Solutions to Inverse Problems of ODEs 349358
- 4. Self-Similarity 350359
- 5. A Derivative Corresponding to the Box-Counting Dimension 353362
- 6. Representation Theory of Fractal Sets 354363
- 7. Spacelike Cantor Sets in a Toy Model 355364
- 8. Concluding Remarks and Future Directions 356365
- References 356365

- Economics and Psychology. Perfect Rationality versus Bounded Rationality 359368