Further Developments in Fractals and Related Fields: Mathematical Foundations and Connections

ISBN-13: 9780817683993 / Angielski / Twarda / 2013 / 288 str.

Julien Barral; St Phane Seuret; Stephane Seuret

Opis

This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, "Fractals and Related Fields II," held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications. The chapters cover fields related to fractals such as: *geometric measure theory*ergodic theory*dynamical systems*harmonic and functional analysis*number theory*probability theoryFurther Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research.

Spis treści

The Rauzy Gasket.- On the Hausdorff Dimension of Graphs of Prevalent Continuous Functions on Compact Sets.- Hausdorff Dimension and Diophantine Approximation.- Singular Integrals on Self-Similar Subsets of Metric Groups.- Multivariate Davenport Series.- Dimensions of Self-Affine Sets.- The Multifractal Spectra of V-Statistics.- Projections of Measures Invariant Under the Geodesic Flow.- Multifractal Tubes.- The Multiplicative Golden Mean Shift has Infinite Hausdorff Measure.- The Law of Iterated Logarithm and Equilibrium Measures Versus Hausdorff Measures For Dynamically Semi-Regular Meromorphic Functions.- Cookie-Cutter-Like Sets with Graph Directed Construction.- Recent Developments on Fractal Properties of Gaussian Random Fields.