Fractal geometry and stochastics iii.分数维几何和StochasticsIII

2004-9  

Bandt, C.; Bandt, Christoph; Mosco, Umberto  

262  

Fractal geometry is used to model complicated natural and technical phenomena in various disciplines like physics，biology，finance，and medicine。 Since most convincing models contain an element of randomness，stochastics enters the area in a natural way。This book documents the establishment of fractal geometry as a substantial mathematical theory。As in the previous volumes，which appeared in 1998 and 2000，leading experts known for clear exposition were selected as authors。They survey their field of expertise，emphasizing recent developments and open problems。 Main topics include multifractal measures， dynamical systems， stochastic processes and random fractals， harmonic analysis on fractals。

PrefaceIntroduction1 Fractal Sets and Measures Markov operators and semifractals by Andrzej Lasota and Jozef Myjak and Tomasz Szarek On various multifractal spectra by Jacques Levy Vehel and Claude Tricot 23 One-dimensional Moran sets and the spectrum of Schrodinger operators by Zhi-Ying Wen 2 Fractals and Dynamical Systems Small-scale structure via flows by Albert M. Fisher Hausdorff dimension of hyperbolic attractors in [Reimann integral][superscript 3] by Karoly Simon The exponent of convergence of Kleinian groups；　on a theorem of Bishop and Jones by Bernd O. Stratmann Lyapunov exponents are not rigid with respect to arithmetic subsequences 3 Stochastic Processes and Random fractals Some topics in the theory of multiplicative chaos by Ai Hua Fan Intersection exponents and the multifractal spectrum for measures on Brownian paths by Peter Morters Additive Levy processes : capacity and Hausdorff dimension 4 Fractal Analysis in Euclidean Space The fractal Laplacian and multifractal quantities by Hans Triebel Geometric representations of currents and distributions by Jenny Harrison Variational principles and transmission conditions for fractal layers 5 Harmonic Analysis on Fractals Function spaces and stochastic processes on fractals by Takashi Kumagai A Dirichlet form on the Sierpinski gasket， related function spaces， and traces by Alf Jonsson Spectral zeta function of symmetric fractals by Alexander Teplyaev

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