04459nam 2200553 450 991082915890332120220902010503.01-4704-1083-4(CKB)3780000000000212(EBL)3113271(SSID)ssj0001339195(PQKBManifestationID)11770509(PQKBTitleCode)TC0001339195(PQKBWorkID)11349989(PQKB)10627054(MiAaPQ)EBC3113271(RPAM)17736024(PPN)19710245X(EXLCZ)99378000000000021220140613h20132013 uy 0engur|n|---|||||txtccrFractal geometry and dynamical systems in pure and applied mathematics II fractals in applied mathematics /David Carfi [and three others], editorsProvidence, Rhode Island :American Mathematical Society,2013.©20131 online resource (384 p.)Contemporary mathematics,1098-3627 ;6010271-4132"PISRS 2011, First International Conference : Analysis, Fractal Geometry, Dynamical Systems and Economics, November 8-12, 2011, Messina, Sicily, Italy.""AMS Special Session, in memory of Benoit Mandelbrot : Fractal Geometry in Pure and Applied Mathematics, January 4-7, 2012, Boston, Massachusetts.""AMS Special Session : Geometry and Analysis on Fractal Spaces, March 3-4, 2012, Honolulu, Hawaii."0-8218-9148-0 Includes bibliographical references.Preface -- Statistical Mechanics and Quantum Fields on Fractals -- 1. Introduction -- 2. Discrete scaling symmetry - Self similarity - Definitions -- 3. Heat kernel and spectral functions - Generalities -- 4. Laplacian on fractals - Heat kernel and spectral zeta function -- 5. Thermodynamics on photons : The fractal blackbody [34] -- 6. Conclusion and some open questions -- Acknowledgments -- References -- Spectral Algebra of the Chernov and Bogoslovsky Finsler Metric Tensors -- Preliminaries -- 1. Spectral theory prerequisites -- 2. Spectral results for low dimensions -- 3. Conclusions -- References -- Local Multifractal Analysis -- 1. Introduction -- 2. Properties of the local Hausdorff dimension and the local multifractal spectrum -- 3. A local multifractal formalism for a dyadic family -- 4. Measures with varying local spectrum -- 5. Local spectrum of stochastic processes -- 6. Other regularity exponents characterized by dyadic families -- 7. A functional analysis point of view -- Acknowledgement -- References -- Extreme Risk and Fractal Regularity in Finance -- 1. Introduction -- 2. Fractal Regularities in Financial Markets -- 3. The Markov-Switching Multifractal (MSM) -- 4. Pricing Multifractal Risk -- 5. Conclusion -- References -- An Algorithm for Dynamical Games with Fractal-Like Trajectories -- 1. Introduction -- 2. Preliminaries and notations -- 3. The method for ¹ games -- 4. Two players parametric games -- 5. The algorithm -- 6. Examples -- 7. Final Remarks -- 8. Resume -- 9. Conclusions -- References -- The Landscape of Anderson Localization in a Disordered Medium -- 1. Introduction -- 2. Preliminaries -- Non-Regularly Varying and Non-Periodic Oscillation of the On-Diagonal Heat Kernels on Self-Similar Fractals -- 1. Introduction -- 2. Framework and main results -- 3. Proof of Theorems 2.17 and 2.18 -- 4. Post-critically finite self-similar fractals -- 4.1. Harmonic structures and resulting self-similar Dirichlet spaces -- 4.2. Cases with good symmetry and affine nested fractals -- 4.3. Cases possibly without good symmetry -- 5. SierpiÅ?ski carpets -- References -- Lattice Effects in the Scaling Limit of the Two-Dimensional Self-Avoiding Walk -- 1. Introduction -- 2. Lattice effects.Contemporary mathematics (American Mathematical Society).6010271-4132FractalsCongressesFractals514/.74228A1228A7828A8011M2611M4137A4537C4537F1058B2058C40mscCarfi David1971-MiAaPQMiAaPQMiAaPQBOOK9910829158903321Fractal geometry and dynamical systems in pure and applied mathematics II3969458UNINA