Fractal geometry and applications: a jubilee of Benoiit Mandelbrot: analysis, number theory, and dynamical systems / ed. by Lapidus M.L., van Frankenhuijsen M. - Providence: American Mathematical Society, 2004. - 517 p.: ill. - (Proceedings of symposia in pure mathematics; vol.72, part.l). - Ref.: p.516-517. - ISBN 0-8218-3637-4  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Part 1. Analysis, Number Theory, and Dynamical Systems Preface ........................................................ ix List of Tributes ............................................... xi Fractal geometry and applications—An introduction to this volume Michel L. Lapidus ............................................ 1 Tributes ....................................................... 27 ANALYSIS Reflections, ripples and fractals Michel Mendes France ........................................ 67 Lacunarity, Minkowski content, and self-similar sets in R Marc Frantz ................................................. 77 Fractals and geometric measure theory: Friends and foes Frank Morgan ................................................ 93 Eigenmeasures, equidistribution, and the multiplicity of β-expansions Hillel Furstenberg and Yitzhak Katznelson ................... 97 Distances on topological self-similar sets Atsushi Kameyama ........................................... 117 Energy and Laplacian on the Sierpinski gasket Alexander Teplyaev ......................................... 131 Electrical networks, symplectic reductions, and application to the renormalization map of self-similar lattices Christophe Sabot .............................................. 155 Notes on Bernoulli convolutions Boris Solomyak ............................................. 207 NUMBER THEORY Some connections between Bernoulli convolutions and analytic number theory Titus Hilberdink ....................... 233 On Davenport expansions Stephane Jaffard ........................................... 273 Hausdorff dimension and Diophantine approximation M. Maurice Dodson and Simon Kristensen ..................... 305 Fractality, self-similarity and complex dimensions Michel L. Lapidus and Machiel van Frankenhuijsen ........... 349 DYNAMICAL SYSTEMS The invariant fractals of symplectic piecewise affine elliptic dynamics Byungik Kahng .............................................. 375 Almost sure rotation number of circle endomorphisms Sylvain Crovisier .......................................... 391 Kneading determinants and transfer operators in higher dimensions Viviane Baladi ............................................. 407 The spectrum of dimensions for Poincare recurrences for nonuniformly hyperbolic geometric constructions Valentin Afraimovich, Leticia Ramirez, and Edgardo Ugalde ..................................................... 417 A Survey of results in random iteration Mark Comerford ............................................. 435 On fibers and local connectivity of Mandelbrot and Multibrot sets Dierk Schleicher ........................................... 477