افق‌های هندسه فراکتالی و ابعاد پیچیده: مدرسه تابستانی 2016 در هندسه فراکتالی و ابعاد پیچیده، به مناسبت شصتمین سالگرد میشل لاپیدوس، 21-29 ژوئن 2016، دانشگاه پلی‌تکنیک کالیفرنیا، سن لوئیس اوبیسپو، کالیفرنیا

This volume contains the proceedings of the 2016 Summer School on Fractal Geometry and Complex Dimensions, in celebration of Michel L. Lapidus's 60th birthday, held from June 21–29, 2016, at California Polytechnic State University, San Luis Obispo, California. The theme of the contributions is fractals and dynamics and content is split into four parts, centered around the following themes: Dimension gaps and the mass transfer principle, fractal strings and complex dimensions, Laplacians on fractal domains and SDEs with fractal noise, and aperiodic order (Delone sets and tilings). Contents 6 Preface: Horizons of Fractal Geometry and Complex Dimensions 8 List of Participants 12 The Mass Transference Principle: Ten years on 16 A measure-theoretic result for approximation by Delone sets 50 Self-similar tilings of fractal blow-ups 56 Regularly varying functions, generalized contents, and the spectrum of fractal strings 78 Dimensions of limit sets of Kleinian groups 110 The spectral operator and resonances 130 Measure-geometric Laplacians for discrete distributions 148 An overview of complex fractal dimensions: from fractal strings to fractal drums, and back 158 Eigenvalues of the Laplacian on domains with fractal boundary 282 Forward integrals and SDE with fractal noise 294 Horizons,of,Fractal,Geometry,and,Complex,Dimensions "This volume contains the proceedings of the 2016 Summer School on Fractal Geometry and Complex Dimensions ... The theme of the contributions is fractals and dynamics and content is split into four parts, centered around the following themes: Dimension gaps and the mass transfer principle, fractal strings and complex dimensions, Laplacians on fractal domains and SDEs with fractal noise, and aperiodic order (Delone sets and tilings)."--Back cover Contains the proceedings of the 2016 Summer School on Fractal Geometry and Complex Dimensions, held in June 2016. Content is split into dimension gaps and the mass transfer principle, fractal strings and complex dimensions, Laplacians on fractal domains and SDEs with fractal noise, and aperiodic order (Delone sets and tilings).