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Fractal Geometry and Stochastics III

Fractal Geometry and Stochastics III
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Field name Details
Dewey Class 516
Title Fractal Geometry and Stochastics III ([EBook] /) / edited by Christoph Bandt, Umberto Mosco, Martina Zähle.
Added Personal Name Bandt, Christoph editor.
Mosco, Umberto editor.
Zähle, Martina editor.
Other name(s) SpringerLink (Online service)
Publication Basel : : Birkhäuser Basel : : Imprint: Birkhäuser, , 2004.
Physical Details X, 262 p. : online resource.
Series Progress in probability ; 57
ISBN 9783034878913
Summary Note 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.:
Contents note 1. Fractal Sets and Measures -- Markov Operators and Semifractals -- On Various Multifractal Spectra -- One-Dimensional Moran Sets and the Spectrum of Schrödinger Operators -- 2. Fractals and Dynamical Systems -- Small-scale Structure via Flows -- Hausdorff Dimension of Hyperbolic Attractors in $$ {\mathbb{R} 3}$$ -- The Exponent of Convergence of Kleinian Groups; on a Theorem of Bishop and Jones -- Lyapunov Exponents Are not Rigid with Respect to Arithmetic Subsequences -- 3. Stochastic Processes and Random fractals -- Some Topics in the Theory of Multiplicative Chaos -- Intersection Exponents and the Multifractal Spectrum for Measures on Brownian Paths -- Additive Lévy Processes: Capacity and Hausdorff Dimension -- 4. Fractal Analysis in Euclidean Space -- The Fractal Laplacian and Multifractal Quantities -- Geometric Representations of Currents and Distributions -- Variational Principles and Transmission Conditions for Fractal Layers -- 5. Harmonic Analysis on Fractals -- Function Spaces and Stochastic Processes on Fractals -- A Dirichlet Form on the Sierpinski Gasket, Related Function Spaces, and Traces -- Spectral Zeta Function of Symmetric Fractals.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
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