By Christoph Bandt, Kenneth Falconer, Martina Zähle
This ebook collects major contributions from the 5th convention on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The e-book is split into 5 topical sections: geometric degree thought, self-similar fractals and recurrent buildings, research and algebra on fractals, multifractal thought, and random buildings. every one half starts off with a state of the art survey through papers overlaying a particular element of the subject. The authors are top international specialists and current their themes comprehensibly and attractively. either newbies and experts within the box will make the most of this book.
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Additional info for Fractal Geometry and Stochastics V
Ledrappier, Singularity of projections of 2dimensional measures invariant under the geodesic flow. Commun. Math. Phys. 312, 127–136 (2012) 24 K. Falconer et al. 37. R. Hovila, E. Järvanpää, M. Järvanpää, F. Ledrappier, Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces. Geom. Dedicata 161, 51–61 (2012) 38. D. Howroyd, Box and packing dimensions of projections and dimension profiles. Math. Proc. Camb. Philos. Soc. 130, 135–160 (2001) 39. X. J. Taylor, Fractal properties of products and projections of measures in Rd .
P. Mattila, Recent progress on dimensions of projections, in Geometry and Analysis of Fractals, ed. -J. -S. Lau. Springer Proceedings in Mathematics & Statistics, vol. 88 (Springer, Berlin/Heidelberg, 2014), pp. 283–301 62. P. Mattila, Fourier Analysis and Hausdorff Dimension (Cambridge University Press, Cambridge, 2015) 63. M. Oberlin, Restricted Radon transforms and projections of planar sets. Can. Math. Bull. 55, 815–820 (2012) Sixty Years of Fractal Projections 25 64. M. Oberlin, Exceptional sets of projections, unions of k-planes and associated transforms.
Vágó, Projections of Mandelbrot percolation in higher dimensions. Ergod. Theory Dyn. Syst. (2014, to appear). 2225 84. C. Tricot, Two definitions of fractional dimension. Math. Proc. Camb. Philos. Soc. 91, 57–74 (1982) 85. Y. Xiao, Packing dimension of the image of fractional Brownian motion. Stat. Probab. Lett. 333, 379–387 (1997) 86. M. Zähle, The average fractal dimension and projections of measures and sets in Rn . Fractals 3, 747 (1995) Scenery Flow, Conical Densities, and Rectifiability Antti Käenmäki Abstract We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces.