Ebook: Further Developments in Fractals and Related Fields: Mathematical Foundations and Connections
- Tags: Geometry, Abstract Harmonic Analysis, Functional Analysis, Partial Differential Equations, Dynamical Systems and Ergodic Theory, Probability Theory and Stochastic Processes
- Series: Trends in Mathematics
- Year: 2013
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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 theory
Further 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.
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 theory
Further 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.
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 theory
Further 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.
Content:
Front Matter....Pages i-xiii
The Rauzy Gasket....Pages 1-23
On the Hausdorff Dimension of Graphs of Prevalent Continuous Functions on Compact Sets....Pages 25-34
Hausdorff Dimension and Diophantine Approximation....Pages 35-45
Singular Integrals on Self-similar Subsets of Metric Groups....Pages 47-61
Multivariate Davenport Series....Pages 63-113
Dimensions of Self-affine Sets: A Survey....Pages 115-134
The Multifractal Spectra of V-Statistics....Pages 135-151
Projections of Measures Invariant Under the Geodesic Flow....Pages 153-160
Multifractal Tubes....Pages 161-191
The Multiplicative Golden Mean Shift Has Infinite Hausdorff Measure....Pages 193-212
The Law of Iterated Logarithm and Equilibrium Measures Versus Hausdorff Measures for Dynamically Semi-regular Meromorphic Functions....Pages 213-234
Cookie-Cutter-Like Sets with Graph-Directed Construction....Pages 235-254
Recent Developments on Fractal Properties of Gaussian Random Fields....Pages 255-288
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 theory
Further 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.
Content:
Front Matter....Pages i-xiii
The Rauzy Gasket....Pages 1-23
On the Hausdorff Dimension of Graphs of Prevalent Continuous Functions on Compact Sets....Pages 25-34
Hausdorff Dimension and Diophantine Approximation....Pages 35-45
Singular Integrals on Self-similar Subsets of Metric Groups....Pages 47-61
Multivariate Davenport Series....Pages 63-113
Dimensions of Self-affine Sets: A Survey....Pages 115-134
The Multifractal Spectra of V-Statistics....Pages 135-151
Projections of Measures Invariant Under the Geodesic Flow....Pages 153-160
Multifractal Tubes....Pages 161-191
The Multiplicative Golden Mean Shift Has Infinite Hausdorff Measure....Pages 193-212
The Law of Iterated Logarithm and Equilibrium Measures Versus Hausdorff Measures for Dynamically Semi-regular Meromorphic Functions....Pages 213-234
Cookie-Cutter-Like Sets with Graph-Directed Construction....Pages 235-254
Recent Developments on Fractal Properties of Gaussian Random Fields....Pages 255-288
....