By Julien Barral, Stéphane Seuret

This quantity, following within the culture of the same 2010 e-book via a similar editors, is an outgrowth of a global convention, "Fractals and similar Fields II," held in June 2011. The booklet presents readers with an summary of advancements within the mathematical fields concerning fractals, together with unique examine contributions in addition to surveys from the various best specialists on smooth fractal conception and functions. learn more... The Rauzy Gasket / Pierre Arnoux, Štěpán Starosta -- at the Hausdorff measurement of Graphs of regular non-stop features on Compact units / Frédéric Bayart, Yanick Heurteaux -- Hausdorff measurement and Diophantine Approximation / Yann Bugeaud -- Singular Integrals on Self-similar Subsets of Metric teams / Vasilis Chousionis, Pertti Mattila -- Multivariate Davenport sequence / Arnaud Durand, Stéphane Jaffard -- Dimensions of Self-affine units: A Survey / Kenneth Falconer -- The Multifractal Spectra of V-Statistics / Ai-hua Fan, Jörg Schmeling, Meng Wu -- Projections of Measures Invariant below the Geodesic stream / Maarit Järvenpää -- Multifractal Tubes / Lars Olsen -- The Multiplicative Golden suggest Shift Has endless Hausdorff degree / Yuval Peres, Boris Solomyak -- The legislations of Iterated Logarithm and Equilibrium Measures as opposed to Hausdorff Measures for Dynamically Semi-regular Meromorphic features / Bartłomiej Skorulski, Mariusz Urbański -- Cookie-Cutter-Like units with Graph-Directed building / Shen Fan, Qing-Hui Liu, Zhi-Ying Wen -- fresh advancements on Fractal houses of Gaussian Random Fields / Yimin Xiao

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Diophantine approximation and Hausdorff dimension. Proc. London Math. Soc. 21, 1–11 (1970) 3. : Ubiquity and large intersections properties under digit frequencies constraints. Math. Proc. Cambridge Philos. Soc. 145, 527–548 (2008) 4. : On approximation of real numbers by real algebraic numbers. Acta Arith. 90, 97–112 (1999) 5. : Rational points near manifolds and metric Diophantine approximation. Ann. Math. 175, 187–235 (2012) 6. : Measure theoretic laws for limsup sets. Mem. Amer. Math. Soc.

Based on earlier work of many people Theorem 1 gives the following corollary: Corollary 1. Let E be a compact 1-regular subset of the complex plane. The following three conditions are equivalent: 1. E is removable for bounded analytic functions. 2. E is removable for Lipschitz harmonic functions. 3. E is purely unrectifiable. Here the pure unrectifiablity of E means that E meets every rectifiable curve in zero length. The removability of E for bounded analytic functions means that if E is contained in an open set U, any bounded analytic function in U \ E can be extended analytically to U.

49(3), 403–442 (2009) 7. : Episturmian words and episturmian morphisms. Theoret. Comput. Sci. 276(1-2), 281–313 (2002). 1016/S0304-3975(01)00207-9 8. : Ergodic properties of a dynamical system arising from percolation theory. Ergod. Theor. Dyn. Syst. 15, 653–661 (1995) 9. : Dimension and measures for a curvilinear Sierpi´nski gasket or Apollonian packing. Adv. Math. 136(1), 26–38 (1998) The Rauzy Gasket 23 10. : Hausdorff dimension and conformal dynamics III: computation of dimension. Am. J. Math.