- Hölder differentiability of self-conformal devil's staircases
2013/01/07 by Sascha Troscheit, SASCHA TROSCHEIT · 1 citation
Mathematics · Physics and Astronomy · #Differentiable function #Dimension function #Effective dimension #Hausdorff dimension #Hausdorff distance #Hausdorff measure #Iterated function system #Mathematical Dynamics and Fractals #Multifractal system #Probability distribution #Probability measure #Statistical Mechanics and Entropy #Theoretical and Computational Physics #math.DS #msc:26A27 #msc:28A80 #msc:37C45 #msc:37D35
- Increasing digit subsystems of infinite iterated function systems
2010/10/25 by Thomas Jordan, Jordan, Thomas, Michal Rams +1 · 1 citation
Mathematics · #Combinatorics #Dimension (graph theory) #Dimension function #Discrete mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Fractal #Fractal dimension #Function (biology) #Hausdorff dimension #Hausdorff space #Iterated function #Iterated function system #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Minkowski–Bouligand dimension #Packing dimension #math.DS
- The Spectral Dimension of Generic Trees
2006/07/11 by Bergfinnur Durhuus, Thordur Jonsson, Thórdur Jónsson +2 · 8 citations
Computer Science · Mathematics · Physics and Astronomy · #Bounded function #Branching (polymer chemistry) #Combinatorics #Dimension (graph theory) #Dimension function #Discrete mathematics #Effective dimension #Exponent #Exponential function #Fractal #Fractal dimension #Graph theory and applications #Hausdorff dimension #Mathematical analysis #Mathematics #Minkowski–Bouligand dimension #Packing dimension #Physics #Statistical physics #Theoretical and Computational Physics #Topological and Geometric Data Analysis #Tree (set theory) #hep-th #math-ph #math.MP #math.PR
- One-sided multifractal analysis and points of non-differentiability of devil's staircases
2004/01/01 by K. J. Falconer · 3 citations
Mathematics · #Mathematical Dynamics and Fractals #Multifractal system #Hausdorff dimension #Differentiable function #Mathematics #Dimension (graph theory) #Context (archaeology) #Fractal dimension #Property (philosophy) #Set (abstract data type) #Dimension function #Effective dimension #Function (biology) #Affine transformation #Pure mathematics #Fractal #Mathematical analysis #Computer science #Geology
- The rate-distortion dimension of sets and measures
1994/01/01 by Tsutomu Kawabata, Amir Dembo · 2 citations
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Computability, Logic, AI Algorithms #Chaos-based Image/Signal Encryption #Minkowski–Bouligand dimension #Mathematics #Packing dimension #Hausdorff dimension #Dimension (graph theory) #Distortion (music) #Fractal dimension #Effective dimension #Dimension function #Upper and lower bounds #Combinatorics #Inductive dimension #Metric (unit) #Sufficient dimension reduction #Distribution (mathematics) #Fractal #Discrete mathematics #Mathematical analysis #Computer science
- Fractal Geometry: Mathematical Foundations and Applications.
1990/09/01 by K. J. Falconer, K. Falconer · 417 citations
Mathematics · #Brownian motion #Computer science #Dimension function #Dynamical systems theory #Effective dimension #Fractal #Fractal analysis #Fractal dimension #Fractal dimension on networks #Fractal landscape #Fractional Brownian motion #Hausdorff dimension #Hausdorff measure #Julia set #Mandelbrot set #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Measure (data warehouse) #Multifractal system
- Evaluating the fractal dimension of profiles
1989/02/01 by Benoit Dubuc, J.F. Quiniou, C. Roques‐Carmes +2 · 4 citations
Mathematics · Physics and Astronomy · Computer Science · #Mathematical Dynamics and Fractals #Theoretical and Computational Physics #Digital Image Processing Techniques #Minkowski–Bouligand dimension #Fractal dimension #Dimension (graph theory) #Effective dimension #Mathematics #Hausdorff dimension #Fractal dimension on networks #Fractional Brownian motion #Multifractal system #Fractal #Fractal analysis #Mandelbrot set #Mathematical analysis #Dimension function #Intersection (aeronautics) #Fractal landscape #Correlation dimension #Brownian motion #Pure mathematics #Statistics
- Can one hear the dimension of a fractal?
1986/03/01 by Jean Brossard, Ren� Carmona · 3 citations
Computer Science · Mathematics · #Boundary (topology) #Bounded function #Combinatorics #Conjecture #Dimension (graph theory) #Dimension function #Fractal #Fractal dimension #Geometry #Hausdorff dimension #Hausdorff measure #Laplace operator #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Measure (data warehouse) #Minkowski space #Minkowski–Bouligand dimension #Partition (number theory) #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum mechanics #Spectral Theory in Mathematical Physics #Topological and Geometric Data Analysis
- Gaussian sample functions and the Hausdorff dimension of level crossings
1970/01/01 by Steven Orey · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Combinatorics #Dimension (graph theory) #Dimension function #Discrete mathematics #Effective dimension #Fractal #Fractal dimension #Function (biology) #Gaussian #Gaussian process #Graph #Hausdorff dimension #Hausdorff measure #Hausdorff space #Mathematical analysis #Mathematics #Minkowski–Bouligand dimension #Morphological variations and asymmetry #Packing dimension #Physics #Quantum mechanics