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Fractal geometry and applications : [electronic resource] a jubilee of Beno�it Mandelbrot / Michel L. Lapidus (managing editor), Machiel van Frankenhuijsen, editors.

Contributor(s): Mandelbrot, Benoit B | Lapidus, Michel L. (Michel Laurent), 1956- | Van Frankenhuysen, Machiel, 1967-Material type: Text

TextSeries: Proceedings of symposia in pure mathematics ; v. 72.1Publication details: Providence, R.I. : American Mathematical Society, c2004Description: 1 online resource (2 v. : ill.)ISBN: 9780821893777 (online)Subject(s): Measure theory -- Congresses | Fractals -- Congresses | Ergodic theory -- CongressesAdditional physical formats: Fractal geometry and applications :DDC classification: 510 LOC classification: QA325 | .F73 2004Online resources: Contents | Contents

Contents:

Fractal geometry and applications -- An introduction to this volume / Michel L. Lapidus -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/0940 Reflections, ripples and fractals / Michel Mend�es France -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112100 Lacunarity, Minkowski content, and self-similar sets in $\mathbb {R}$ / Marc Frantz -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112101 Fractals and geometric measure theory: friends and foes / Frank Morgan -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112102 Eigenmeasures, equidistribution, and the multiplicity of $\beta $-expansions / Hillel Furstenberg and Yitzhak Katznelson -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112103 Distances on topological self-similar sets / Atsushi Kameyama -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112104 Energy and Laplacian on the Sierpi�nski gasket / Alexander Teplyaev -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112105 Electrical networks, symplectic reductions, and application to the renormalization map of self-similar lattices / Christophe Sabot -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112106 Notes on Bernoulli convolutions / Boris Solomyak -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112107 Some connections between Bernoulli convolutions and analytic number theory / Titus Hilberdink -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112108 On Davenport expansions / St�ephane Jaffard -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112109 Hausdorff dimension and Diophantine approximation / M. Maurice Dodson and Simon Kristensen -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112110 Fractality, self-similarity and complex dimensions / Michel L. Lapidus and Machiel van Frankenhuijsen -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112111 The invariant fractals of symplectic piecewise affine elliptic dynamics / Byungik Kahng -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112112 Almost sure rotation number of circle endomorphisms / Sylvain Crovisier -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112113 Kneading determinants and transfer operators in higher dimensions / Viviane Baladi -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112114 The spectrum of dimensions for Poincar�e recurrences for nonuniformly hyperbolic geometric constructions / Valentin Afraimovich, Leticia Ram�irez and Edgardo Ugalde -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112115 A survey of results in random iteration / Mark Comerford -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112116 On fibers and local connectivity of Mandelbrot and Multibrot sets / Dierk Schleicher -- http://www.ams.org/pspum/072.1 http://dx.doi.org/10.1090/pspum/072.1/2112117

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Includes bibliographical references.

Fractal geometry and applications -- An introduction to this volume / Michel L. Lapidus -- Reflections, ripples and fractals / Michel Mend�es France -- Lacunarity, Minkowski content, and self-similar sets in $\mathbb {R}$ / Marc Frantz -- Fractals and geometric measure theory: friends and foes / Frank Morgan -- Eigenmeasures, equidistribution, and the multiplicity of $\beta $-expansions / Hillel Furstenberg and Yitzhak Katznelson -- Distances on topological self-similar sets / Atsushi Kameyama -- Energy and Laplacian on the Sierpi�nski gasket / Alexander Teplyaev -- Electrical networks, symplectic reductions, and application to the renormalization map of self-similar lattices / Christophe Sabot -- Notes on Bernoulli convolutions / Boris Solomyak -- Some connections between Bernoulli convolutions and analytic number theory / Titus Hilberdink -- On Davenport expansions / St�ephane Jaffard -- Hausdorff dimension and Diophantine approximation / M. Maurice Dodson and Simon Kristensen -- Fractality, self-similarity and complex dimensions / Michel L. Lapidus and Machiel van Frankenhuijsen -- The invariant fractals of symplectic piecewise affine elliptic dynamics / Byungik Kahng -- Almost sure rotation number of circle endomorphisms / Sylvain Crovisier -- Kneading determinants and transfer operators in higher dimensions / Viviane Baladi -- The spectrum of dimensions for Poincar�e recurrences for nonuniformly hyperbolic geometric constructions / Valentin Afraimovich, Leticia Ram�irez and Edgardo Ugalde -- A survey of results in random iteration / Mark Comerford -- On fibers and local connectivity of Mandelbrot and Multibrot sets / Dierk Schleicher --