Horizons of Fractal Geometry and Complex Dimensions
About this Title
Robert G. Niemeyer, Metropolitan State University of Denver, Denver, CO, Erin P. J. Pearse, California Polytechnic State University, San Luis Obispo, CA, John A. Rock, California State Polytechnic University, Pomona, CA and Tony Samuel, California Polytechnic State University, San Luis Obispo, CA, Editors
Publication: Contemporary Mathematics
Publication Year: 2019; Volume 731
ISBNs: 978-1-4704-3581-3 (print); 978-1-4704-5315-2 (online)
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).
Graduate students and research mathematicians interested in fractal geometry, dynamical systems, and related areas.
Table of Contents
- Demi Allen and Sascha Troscheit – The Mass Transference Principle: Ten years on
- Michael Baake and Alan Haynes – A measure-theoretic result for approximation by Delone sets
- M. F. Barnsley and A. Vince – Self-similar tilings of fractal blow-ups
- Tobias Eichinger and Steffen Winter – Regularly varying functions, generalized contents, and the spectrum of fractal strings
- Kurt Falk – Dimensions of limit sets of Kleinian groups
- Machiel van Frankenhuijsen – The spectral operator and resonances
- M. Kesseböhmer, T. Samuel and H. Weyer – Measure-geometric Laplacians for discrete distributions
- Michel L. Lapidus – An overview of complex fractal dimensions: from fractal strings to fractal drums, and back
- Paul Pollack and Carl Pomerance – Eigenvalues of the Laplacian on domains with fractal boundary
- Martina Zähle and Erik Schneider – Forward integrals and SDE with fractal noise