Titlebook: Recent Developments in Fractals and Related Fields; Conference on Fracta Julien Barral,Stéphane Seuret Conference proceedings 2017 Springer

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Julien Barral,Stéphane SeuretProvides an overview of recent developments in mathematical fields related to fractals.Includes original research contributions as well as surveys written by experts in their respective fields.Readers

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Recent Developments in Fractals and Related Fields978-3-319-57805-7Series ISSN 2297-0215 Series E-ISSN 2297-024X

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The Two-Dimensional Density of Bernoulli Convolutions,ich has an intricate combinatorial structure. Visualizing this structure we discuss results of Erd?s, Jóo, Komornik, Sidorov, de Vries, Jordan, Shmerkin and Solomyak, Feng and Wang. We emphasize the role of finite orbits of associated multivalued maps and mention a few new properties and examples.

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Some Recent Developments of Self-Affine Tiles,d a . if it is also a tile, and call such . a .. In this survey, we review some recent developments on the structure and characterizations?of the tile digit sets . for a given .. We also discuss the celebrated Fuglede’s spectral set problem on the self-affine tiles.

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A Class of Random Cantor Measures, with Applications,proofs, yet is general enough for several applications and contains the well-known fractal percolation measure. We study self-convolutions and Fourier decay of measures in our class, and present applications of these results to the restriction problem for fractal measures, and the connection between arithmetic structure and Fourier decay.