Kenneth Falconer

Q: What Schools Are Affiliated With Kenneth Falconer

Kenneth Falconer is affiliated with the following schools: University of St Andrews, University of Bristol, University of Cambridge

Kenneth Falconer 's AcademicInfluence.com Rankings

Kenneth Falconer

Mathematics

#1314

World Rank

#2195

Historical Rank

Measure Theory

#415

World Rank

#601

Historical Rank

mathematics Degrees

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Mathematics

Why Is Kenneth Falconer Influential?

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According to Wikipedia, Kenneth John Falconer FRSE is a British mathematician working in mathematical analysis and in particular on fractal geometry. He is Regius Professor of Mathematics in the School of Mathematics and Statistics at the University of St Andrews.

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Kenneth Falconer 's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Fractal geometry - mathematical foundations and applications (1990) (6722)
Techniques in fractal geometry (1997) (1523)
The geometry of fractal sets (1985) (942)
Unsolved Problems In Geometry (1991) (635)
The geometry of fractal sets: Contents (1985) (527)
GEOMETRY OF SETS AND MEASURES IN EUCLIDEAN SPACES FRACTALS AND RECTIFIABILITY (1996) (458)
The Hausdorff dimension of self-affine fractals (1988) (349)
On the Hausdorff dimensions of distance sets (1985) (211)
Fractal Geometry Mathematical Foundations and Applications Third (2013) (176)
The multifractal spectrum of statistically self-similar measures (1994) (174)
Dimensions and measures of quasi self-similar sets (1989) (143)
On the lipschitz equivalence of Cantor sets (1992) (113)
On the Minkowski measurability of fractals (1995) (99)
The dimension of self-affine fractals II (1992) (98)
The Local Structure of Random Processes (2003) (96)
A subadditive thermodynamic formalism for mixing repellers (1988) (87)
Packing dimensions of projections and dimension profiles (1997) (84)
Bounded distortion and dimension for non-conformal repellers (1994) (82)
Hausdorff dimension and the exceptional set of projections (1982) (79)
Sets with Large Intersection Properties (1994) (78)
Tangent Fields and the Local Structure of Random Fields (2002) (76)
Projection theorems for box and packing dimensions (1996) (65)
Non-linear Elliptical Equations on the Sierpinski Gasket ´ (1999) (65)
Sixty years of fractal projections (2014) (64)
The Realization of Distances in Measurable Subsets Covering Rn (1981) (58)
Classification of a quasi-circles by Hausdorff dimension (1989) (56)
Semilinear PDEs on Self-Similar Fractals (1999) (56)
X‐Ray Problems for Point Sources (1983) (56)
Multifractional, Multistable, and Other Processes with Prescribed Local Form (2008) (56)
Exact dimensionality and projections of random self‐similar measures and sets (2012) (55)
Sub-self-similar sets (1995) (55)
The Hausdorff dimension of some fractals and attractors of overlapping construction (1987) (53)
The packing dimension of projections and sections of measures (1996) (52)
Generalized dimensions of measures on self-affine sets (1999) (49)
DIMENSIONS OF SELF-AFFINE FRACTALS AND MULTIFRACTALS GENERATED BY UPPER-TRIANGULAR MATRICES (2007) (48)
On the geometry of random Cantor sets and fractal percolation (1992) (45)
Applications of a Result on Spherical Integration to the Theory of Convex Sets (1983) (45)
Plane Sets with Positive Density at Infinity Contain all Large Distances (1986) (42)
Continuity properties of k-plane integrals and Besicovitch sets (1980) (40)
Classes of sets with large intersection (1985) (37)
Fractals: A Very Short Introduction (2013) (36)
Dimensions of Self-affine Sets: A Survey (2013) (35)
Nonlinear Diffusion Equations on Unbounded Fractal Domains (2001) (35)
Convolutions and the Geometry of Multifractal Measures (1999) (35)
Planar self-affine sets with equal Hausdorff, box and affinity dimensions (2015) (35)
Wavelet transforms and order-two densities of fractals (1992) (34)
Generalized dimensions of measures on almost self-affine sets (2009) (32)
Cut-set sums and tree processes (1987) (28)
Continuity of Subadditive Pressure for Self-Affine Sets (2009) (28)
Multistable Processes and Localizability (2010) (27)
Sets with Prescribed Projections and Nikodym Sets (1986) (26)
Vector-valued multifractal measures (1996) (25)
On a problem of Erdős on sequences and measurable sets (1984) (25)
The Dimension of the Convex Kernel of a Compact Starshaped Set (1977) (24)
Localizable Moving Average Symmetric Stable and Multistable Processes (2009) (23)
Projections of random Cantor sets (1989) (22)
Symmetry and enumeration of self‐similar fractals (2007) (22)
Localisable moving average stable and multistable processes (2008) (21)
Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes (2015) (21)
Intermediate dimensions (2018) (21)
One-sided multifractal analysis and points of non-differentiability of devil's staircases (2004) (21)
Hammer's X‐Ray Problem and the Stable Manifold Theorem (1983) (20)
Representation of families of sets by measures, dimension spectra and Diophantine approximation (2000) (20)
The horizon problem for prevalent surfaces (2011) (20)
Dixmier traces and coarse multifractal analysis (2009) (19)
Fractal Properties of Generalized Sierpiński Triangles (1998) (19)
The visible part of plane self-similar sets (2010) (18)
Exceptional sets for self-affine fractals (2008) (17)
Dimension Conservation for Self-Similar Sets and Fractal Percolation (2014) (17)
Projection theorems for intermediate dimensions (2019) (16)
Minkowski dimension for measures (2020) (14)
RANDOM SUBSETS OF SELF-AFFINE FRACTALS (2010) (14)
The dimension of projections of self-affine sets and measures (2015) (14)
A Result on the Steiner Symmetrization of a Compact Set (1976) (14)
On a Problem of Erdös on Fractal Combinatorial Geometry (1992) (13)
Dimensions — their determination and properties (1991) (13)
On the equireciprocal point problem (1983) (13)
Average densities of the image and zero set of stable processes (1995) (13)
RANDOM GEOMETRICALLY GRAPH DIRECTED SELF‐SIMILAR MULTIFRACTALS (Pitman Research Notes in Mathematics 307) (1996) (12)
Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure (2011) (12)
Packing dimensions of sections of sets (1999) (12)
Horizons of fractional Brownian surfaces (2000) (12)
The fractal structure of elliptical polynomial spirals (2020) (11)
Sections of Sets of zero Lebesgue measure (1980) (11)
Deterministic Chaos in Infinite Quantum Systems (trieste Notes in Physics) (11)
Rings of fractional dimension (1984) (11)
A capacity approach to box and packing dimensions of projections of sets and exceptional directions (2019) (11)
Order-two density of sets and measures with non-integral dimension (1995) (10)
The Realization of small Distances in Plane Sets of Positive Measure (1986) (10)
The Influence of Benoît B. Mandelbrot on mathematics (2012) (9)
The Hausdorff dimension of pulse-sum graphs (2007) (9)
Growth rate of an endomorphism of a group (2011) (9)
A Capacity Approach to Box and Packing Dimensions of Projections and Other Images (2017) (8)
Singularities of sets of constant width (1981) (8)
Intersections of thick compact sets in R d (2022) (8)
Consistency conditions for a finite set of projections of a function (1979) (7)
Dimensions of intersections and distance sets for polyhedral norms. (2005) (7)
The critical point of fractal percolation in three and more dimensions (1991) (7)
Differentiation of the Limit Mapping in a Dynamical System (1983) (7)
Intermediate Dimensions: A Survey (2020) (7)
Local dimensions of measures on self-affine sets (2011) (7)
Digital sundials, paradoxical sets, and vitushkin’s conjecture (1987) (7)
Inference on fractal processes using multiresolution approximation (2007) (7)
A Characterisation of Plane Curves of Constant Width (1977) (7)
Hausdorff Measure and Dimension (2005) (6)
Examples Illustrating the Instability of Packing Dimensions of Sections (1999) (6)
Generalized dimensions of images of measures under Gaussian processes (2012) (6)
Inhomogeneous parabolic equations on unbounded metric measure spaces (2011) (6)
Function space topologies defined by sectional integrals and applications to an extremal problem (1980) (5)
Marstrand's Theorem revisited: Projecting sets of dimension zero (2017) (5)
Assouad dimension influences the box and packing dimensions of orthogonal projections (2019) (5)
Codimension formulae for the intersection of fractal subsets of Cantor spaces (2014) (5)
Packing and Covering (1991) (5)
The horizon problem for random surfaces (1991) (5)
Applications of outwardly simple line families to plane convex sets (1977) (4)
Intersections of thick compact sets in $${\mathbb {R}}^d$$ (2021) (4)
The dimension of affine-invariant fractals (1988) (4)
Projections, slices and dimension conservation for random self-similar measures and sets (2012) (4)
$L^{q}$ -spectra of measures on planar non-conformal attractors (2020) (4)
On the geometry of random cantor sets and fractal percolation (1994) (4)
Self-stabilizing processes (2018) (3)
Intermediate dimension of images of sequences under fractional Brownian motion (2021) (3)
Fractal Geometry and Analysis (1991) (3)
Fractals, Wavelets, and their Applications (2014) (3)
Exact dimensionality and projection properties of Gaussian multiplicative chaos measures (2016) (3)
The Ancient English Art of Change Ringing (1994) (2)
A Hölder-type inequality on a regular rooted tree (2014) (2)
On maximal Euclidean sets avoiding certain distance configurations (1981) (2)
The determination of a function from its projections (1979) (2)
Probabilistic Methods in Fractal Geometry (1995) (2)
General Geometric Problems (1991) (2)
Growth conditions on powers of Hermitian elements (1982) (2)
Self-Stabilizing Processes Based on Random Signs (2018) (2)
Measure, topology and fractal geometry , by Gerald A. Edgar. Pp 230. DM58. 1990. ISBN 3-540-97272-2 (Springer) (1991) (2)
Fubini-type theorems for general measure constructions (2000) (2)
Iteration of Complex Functions—Julia Sets (2005) (2)
The geometry of fractal sets: Measure and dimension (1985) (1)
H\"older continuity of the Liouville Quantum Gravity measure (2016) (1)
Projections of Fractals (2005) (1)
From fractional Brownian motion to multifractional and multistable motion (2015) (1)
The geometry of fractal sets: Introduction (1985) (1)
The density of sets containing large similar copies of finite sets (2020) (1)
Alternative Definitions of Dimension (2005) (1)
Fractals. Non-Integral Dimensions and Applications, G. Gherbit (Ed.). John Wiley, New York (1991), 249 (1991) (1)
Brownian Motion and Brownian Surfaces (2005) (1)
6. Fractals in the real world (2013) (1)
Finite Sets of Points (1991) (1)
Claude Ambrose Rogers. 1 November 1920 — 5 December 2005 (2015) (1)
Absolute continuity of projections of Gaussian multiplicative chaos measures (2016) (1)
7. A little history (2013) (1)
Dimensions, Dynamics and Cutting up Ellipses (1998) (1)
Notation and Definitions (1991) (1)
Local Structure of Fractals (2005) (1)
CHAPTER 25 – Fractal Measures (2002) (1)
Generalized energy inequalities and higher multifractal moments (2014) (0)
The geometry of fractal sets: Projection properties (1985) (0)
Intersections of Fractals (2005) (0)
Self-stabilizing processe (2018) (0)
5. Random walks and Brownian motion (2013) (0)
Self-Stabilizing Processes Based on Random Signs (2018) (0)
Dimensions of fractals and multifractals (1998) (0)
The geometry of fractal sets: Miscellaneous examples of fractal sets (1985) (0)
Number Theory and Dynamical Systems: The integral geometry of fractals (1989) (0)
A Nonlinear Mercerian Theorem (1999) (0)
The geometry of fractal sets: Notation (1985) (0)
Richard Kenneth Guy, 1916–2020 (2022) (0)
On circle averages of Gaussian free fields and Liouville quantum gravity (2016) (0)
Book Reviews: Chaos and Fractals, A Computer Graphical Journey (1998) (0)
1. The fractal concept (2013) (0)
The geometry of fractal sets: References (1985) (0)
Higher moments for random multiplicative measures (2013) (0)
A Nightmare Seminar (2009) (0)
Confessions of a Non-Joiner (1967) (0)
The geometry of fractal sets: Besicovitch and Kakeya sets (1985) (0)
Fractals, Wavelets, and their Applications : Contributions from the International Conference and Workshop on Fractals and Wavelets (2014) (0)
On the convergence of certain singular integrals (1981) (0)
Examples from Number Theory (2005) (0)
BSHM Meeting News (2022) (0)
The geometry of fractal sets: Basic density properties (1985) (0)
Intermediate dimensions (2019) (0)
G. David and S. Semmes Fractured fractals and broken dreams – self-similar geometry through metric and measure (Oxford Lecture Series in Mathematics and its Applications Vol. 7, Clarendon Press, Oxford, 1997), ix + 212pp., 0 19 850166 8, (hardback) £35. (1999) (0)
Sets with large density at infinity contain all large copies of finite sets (2020) (0)
The geometry of fractal sets: Structure of sets of non-integral dimension (1985) (0)
4. Julia sets and the Mandelbrot set (2013) (0)
Polygons, Polyhedra, and Polytopes (1991) (0)
The geometry of fractal sets: Comparable net measures (1985) (0)
Lines cutting convex sets in the plane (1981) (0)
Techniques for Calculating Dimensions (2005) (0)
Products of Fractals (2005) (0)
Iterated Function Systems—Self‐Similar and Self‐Affine Sets (2005) (0)
Self-similar sets: Projections, sections and percolation (2015) (0)
Tiling and Dissection (1991) (0)
Box-Counting Dimension in One-Dimensional Random Geometry of Multiplicative Cascades (2022) (0)
2. Self-similarity (2013) (0)
Examples from Pure Mathematics (2005) (0)
N. Steinmetz Rational iteration: complex analytic dynamical systems (de Gruyter Studies in Mathematics Vol. 16, de Gruyter, Berlin, New York 1993) x + 190 pp., 3 11 013765 8, about £60. (1995) (0)
Infinite beauty (2004) (0)
3. Fractal dimension (2013) (0)
Mandelbrot, B. Gaussian self-affinity and fractals---globality, the Earth, 1/f noise, and R/S (Springer, 2002), ix+654 pp., 0 387 98993 5 (hardback), £46 (US$59.95) (2005) (0)
A dichotomy on the self-similarity of graph-directed attractors (2022) (0)
Graphs of Functions (2005) (0)

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What Schools Are Affiliated With Kenneth Falconer ?

Kenneth Falconer is affiliated with the following schools: