LEADER 04459nam 2200553 450 001 9910829158903321 005 20220902010503.0 010 $a1-4704-1083-4 035 $a(CKB)3780000000000212 035 $a(EBL)3113271 035 $a(SSID)ssj0001339195 035 $a(PQKBManifestationID)11770509 035 $a(PQKBTitleCode)TC0001339195 035 $a(PQKBWorkID)11349989 035 $a(PQKB)10627054 035 $a(MiAaPQ)EBC3113271 035 $a(RPAM)17736024 035 $a(PPN)19710245X 035 $a(EXLCZ)993780000000000212 100 $a20140613h20132013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFractal geometry and dynamical systems in pure and applied mathematics II $efractals in applied mathematics /$fDavid Carfi [and three others], editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2013. 210 4$d©2013 215 $a1 online resource (384 p.) 225 1 $aContemporary mathematics,$x1098-3627 ;$v601$x0271-4132 300 $a"PISRS 2011, First International Conference : Analysis, Fractal Geometry, Dynamical Systems and Economics, November 8-12, 2011, Messina, Sicily, Italy." 300 $a"AMS Special Session, in memory of Benoit Mandelbrot : Fractal Geometry in Pure and Applied Mathematics, January 4-7, 2012, Boston, Massachusetts." 300 $a"AMS Special Session : Geometry and Analysis on Fractal Spaces, March 3-4, 2012, Honolulu, Hawaii." 311 $a0-8218-9148-0 320 $aIncludes bibliographical references. 327 $aPreface -- 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 A?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. SierpiA??ski carpets -- References -- Lattice Effects in the Scaling Limit of the Two-Dimensional Self-Avoiding Walk -- 1. Introduction -- 2. Lattice effects. 410 0$aContemporary mathematics (American Mathematical Society).$v601$x0271-4132 606 $aFractals$vCongresses 615 0$aFractals 676 $a514/.742 686 $a28A12$a28A78$a28A80$a11M26$a11M41$a37A45$a37C45$a37F10$a58B20$a58C40$2msc 702 $aCarfi$b David$f1971- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910829158903321 996 $aFractal geometry and dynamical systems in pure and applied mathematics II$93969458 997 $aUNINA