Kenneth Falconer - Books, Papers, Preprints
Links to listingsMathSciNet
BooksThe 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 papersThe 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 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.M. Fraser) The horizon problem for prevalent surfaces, Math. Proc. Cambridge Philos. Soc., 151 (2011), 355-372 , 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 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 Xiong Jin) Dimension conservation for self-similar sets and fractal percolation, Int. Math. Res. Notices, 2015(24) (2015), 13260-13289, 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 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 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
(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
(with J. Fraser and A. Käenmäki) Minkowski dimension for measures, arXiv
(with J. Hu and J. Zhang) A dichotomy on the self-similarity of graph-directed attractors, arXiv