Books, papers & preprints

Some pictures

Fractal sites

Maths sites

Fractal movies

Maths poems


Kenneth Falconer - Books, Papers, Preprints

Links to listings


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The Geometry of Fractal Sets, Cambridge UP, 1985; paperback 1986.

Fractal Geometry - Mathematical Foundations and Applications , John Wiley, Third Edition, 2014, with Solutions Manual 3rd Ed.

Unsolved Problems in Geometry (with H.T. Croft and R.K. Guy), Springer-Verlag, 1991.

Techniques in Fractal Geometry, John Wiley, 1997.

Fractals - A Very Short Introduction, Oxford UP, 2013.

Some selected papers

The Hausdorff dimension of self-affine fractals, Math. Proc. Cambridge Philos. Soc., 103 (1988), 339-350.

The dimension of self-affine fractals II, Math. Proc. Cambridge Philos. Soc., 111 (1992), 169-179.

Bounded distortion and dimension for non-conformal repellers, Math. Proc. Cambridge Philos. Soc. 115 (1994) 315-334.

The multifractal spectrum of statistically self-similar measures, J. Theoretical Probability, 7 (1994) 681-702.

Probabilistic methods in fractal geometry, Proc. Conf. Fractal Geometry and Stochastics, Finsterbergen 1994, Progress in Probability, 37 (1995), 3-13.

(with P. Mattila) The packing dimension of projections and sections of measures, Math. Proc. Cambridge Philos. Soc., 119 (1996), 695-713.

(with T.C. O'Neil) Vector-valued multifractal measures, Proc. Royal. Soc. Ser. A: Math and Phys. Sci., 452 (1996), 1433-1457.

(with J.D. Howroyd) Packing dimensions of projections and dimension profiles, Math. Proc. Cambridge Philos. Soc., 121 (1997), 269-286.

(with B. Lammering) Fractal properties of generalized Sierpinski triangles, Fractals,6 (1998), 31-41.

(with M Järvenpää) Packing dimensions of sections of sets, Math. Proc. Cambridge Philos. Soc., 125(1999), 89-104.

Generalised dimensions of measures on self-affine sets, Nonlinearity, 12(1999), 877-891.

Semilinear PDEs on self-similar fractals, Commun. Math. Phys. 206(1999), 235-245.

A nonlinear Mercerian theorem, J. Math. Anal. App. 239(1999), 440-448.

Representation of families of sets by measures, multifractal analysis and Diophantine approximation, Math. Proc. Cambridge Philos. Soc. 128(2000), 111-121.

(with J. Lévy Véhel) Horizons of fractional Brownian surfaces, Proc. Roy. Soc. London, Ser. A. 456(2000), 2153--2177

(with M. Järvenpää and P. Mattila) Examples illustrating the instability of packing dimensions of sections, Real Analysis Exchange, 25 (2000), 629--640.

(with R.D. Mauldin) Fubini-type theorems for general measure constructions, Mathematika, 47 (2000), 251--265.

(with J. Hu) Nonlinear diffusion equations on unbounded fractal domains, J. Math. Anal. App., 256(2001), 606--624.

Tangent fields and the local structure of random fields, J. Theoret. Probab. 15 (2002), 731--750.

The local structure of random processes, J. London Math. Soc.67 (2003), 657--672.

One-sided multifractal analysis and points of non-differentiability of devil's staircases,  Math. Proc. Cambridge Philos. Soc. 136 (2004), 167-174.

Dimensions of intersections and distance sets for polyhedral norms; Real Analysis Exchange, 30(2005),719--726.

(with J. O'Connor) Symmetry and enumeration of self-similar fractals; Bull. London Math. Soc., 39 (2007), 272-282.

(with C. Fernández) Inference on fractal processes using multiresolution approximation; Biometrika, 94 (2007), 313-334. Preprint

(with Y. Demichel) The Hausdorff dimension of pulse-sum graphs; Math. Proc. Cambridge Philos. Soc., 143 (2007), 145-155. Preprint

(with J. Miao) Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices; Fractals, 15 (2007), 289-299. Preprint

(with J. Miao) Exceptional sets for self-affine fractals; Math. Proc. Cambridge Philos. Soc., 145 (2008), 669-684. Preprint , Cambridge Journals Online

(with J. Lévy Véhel) Multifractional, multistable, and other processes with prescribed local form, J. Theor. Probab., 22 (2009), 375-401. arXiv, SpringerLink DOI: 10.1007/s10959-008-0147-9

(with R. Le Guével and J. Lévy Véhel) Localisable moving average stable and multistable processes, Stochastic Models, 25 (2009), 648-672. arXiv

(with A. Sloan) Continuity of subadditive pressure for self-affine sets, Real Analysis Exchange, 34 (2009), 413-428. Preprint

(with J. Miao) Random subsets of self-affine fractals, Mathematika, 56 (2010), 61-76. Preprint , Cambridge Journals Online

Generalised dimensions of measures on almost self-affine sets, Nonlinearity, 23 (2010), 1047-1069. arXiv , IOPScience link

(with A. Samuel) Dixmier traces and coarse multifractal analysis; Ergodic Theory Dynam. Systems, 31 (2011), 369-381, arXiv

(with J.M. Fraser) The horizon problem for prevalent surfaces, Math. Proc. Cambridge Philos. Soc., 151 (2011), 355-372 , arXiv

(with Lining Liu) Multistable processes and localisability, Stochastic Models 28 (2012), 503-526, arXiv

(with Jiaxin Hu and Yuhua Sun) Inhomogeneous parabolic equations on unbounded metric measure spaces, Proc. Roy. Soc. Edinburgh A Mathematics 142 (2012), 1003-1025 , arXiv

(with J.M. Fraser) The visible part of plane self-similar sets, Proc. American Math. Soc. 141 (2013), 269-278, arXiv

(with G.C. Boore) Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure, Math. Proc. Cambridge Philos. Soc. 154 (2013), 325-349

(with Yimin Xiao) Generalized dimensions of images of measures under Gaussian processes, Adv. Math.252 (2014), 492-517, arXiv

(with Xiong Jin) Exact dimensionality and projections of random self-similar measures and sets, J. London Math. Soc. 90 (2014), 388-412, arXiv

A Holder-type inequality on a regular rooted tree, J. Math. Analysis Appl. 423 (2015), 913-923, arXiv

(with Xiong Jin) Dimension conservation for self-similar sets and fractal percolation, Int. Math. Res. Notices, 2015(24) (2015), 13260-13289, arXiv

Higher moments for random multiplicative measures, J. Fractal Geometry 2 (2015), 229-247, arXiv

(with J.M. Fraser and Xiong Jin) Sixty years of fractal projections, in Fractal Geometry and Stochastics V, Progress in Probability 70, pp.3-25, Birkhauser (2015), arXiv

From fractional Brownian motion to multifractional and multistable motion, in Benoit Mandelbrot - A Life in Many Dimensions, pp.239-256, World Scientific, 2015

(with Casey Donoven) Codimension formulae for the intersection of fractal subsets of Cantor spaces, Proc. Amer. Math. Soc 144 (2016), 651-663, arXiv

(with Pertti Mattila) Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes, J. Fractal Geometry 3 (2016), 319-329, arXiv

(with Tom Kempton) The dimension of projections of self-affine sets and measures, Annales Academiae Scientiarum Fennicae - Mathematica 42 (2017), 473-486, arXiv

(with Tom Kempton) Planar self-affine sets with equal Hausdorff, box and affinity dimensions, Ergodic Theory and Dynamical Systems 38 (2018), 1289-1341, arXiv

(with J. Lévy Véhel) Self-stabilizing processes, Stochastic Models 34 (2018), 409-434, arXiv

(with V. Beresnevich, S. Velani, and A. Zafeiropoulos) Marstrand's Theorem revisited: projecting sets of dimension zero, J. Math. Analysis Appl. 472 (2019), 1820-1845 arXiv

(with Xiong Jin) Exact dimensionality and projection properties of Gaussian multiplicative chaos measures, Trans. Amer. Math. Soc. 372 (2019), 2921-2957 arXiv

(with J. Fraser, and T. Kempton) Intermediate dimensions, Math. Zeit. 296 (2019) arXiv

(with J. Lévy Véhel) Self-stabilizing processes based on random signs, J. Theoret. Probab. 33 (2020), 134-152,

A capacity approach to box and packing dimensions of projections and other images, in Analysis, Probability and Mathematical Physics on Fractals, World Scientific (2020), arXiv

A capacity approach to box and packing dimensions of projections of sets and exceptional directions, J. Fractal Geom. 8 (2021), 1-26 arXiv

(with S. Burrell, and J. Fraser) Projection theorems for intermediate dimensions, J. Fractal Geom. 8 (2021), 95-116 arXiv

(with J. Fraser and P. Shmerkin) Assouad dimension influences the box and packing dimensions of orthogonal projections, J. Fractal Geom. 8 (2021), 247-259 arXiv

(with J. Fraser and L. Lee) Lq-spectra of measures of planar non-conformal atractors, Ergodic Theory Dynam. Systems. 41 (2021), 3288-3306 arXiv

Intermediate dimensions - a survey, Thermodynamic Formalism: CIRM Jean-Morley Chair, Fall 2019. Pollicott, M. & Vaienti, S. (eds.). Springer, 469-493 (Lecture Notes in Mathematics; vol. 2290), 2021. arXiv

Intermediate dimension of images of sequences under fractional Brownian motion, Statist. Probab. Lett. 182 (2021), 109300 arXiv

(with V. Kovac and A. Yavicoli) The density of sets containing large similar copies of finite sets, arXiv, J. d'Analyse Math. 148 (2022), 339-359

(with A. Yavicoli) Intersections of thick compact sets in Rd, arXiv, Math. Zeit. 301 (2022), 2291-2315

(with S. Burrell and J. Fraser ) The fractal structure of elliptical polynomial spirals, arXiv, Monatshefte fur Math. 199 (2022), 1-22,

(with J. Fraser and A. Käenmäki) Minkowski dimension for measures. arXiv, Proc. American Math. Soc. 151 (2023), 779-794

(with S. Troscheit) Box-counting dimension in one-dimensional random geometry of multiplicative cascades. arXiv, Comm. Math. Phys. 399 (2023), 57-83

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