Topology Of Tiling Spaces
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| Author | : Lorenzo Adlai Sadun |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 131 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821847279 |
"This book is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. It isn't a comprehensive and cross-referenced tome about everything having to do with tilings, which would be too big, too hard to read, and far too hard to write! Rather, it is a review of the explosion of recent work on tiling spaces as inverse limits, on the cohomology of tiling spaces, on substitution tilings and the role of rotations, and on tilings that do not have finite local complexity. Powerful computational techniques have been developed, as have new ways of thinking about tiling spaces." "The text contains a generous supply of examples and exercises."--BOOK JACKET.
| Author | : Sherman K. Stein |
| Publisher | : Mathematical Association of America (MAA) |
| Total Pages | : 222 |
| Release | : 2014-05-10 |
| Genre | : MATHEMATICS |
| ISBN | : 9781614440246 |
A concise investigation into the connections between tiling space problems and algebraic ideas, suitable for undergraduates.
| Author | : Johannes Kellendonk |
| Publisher | : Birkhäuser |
| Total Pages | : 438 |
| Release | : 2015-06-05 |
| Genre | : Mathematics |
| ISBN | : 3034809034 |
What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrödinger operators, and connections to arithmetic number theory.
| Author | : András Prékopa |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 497 |
| Release | : 2006-06-03 |
| Genre | : Mathematics |
| ISBN | : 0387295550 |
"From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.
| Author | : Elliott M. Pearl |
| Publisher | : Elsevier |
| Total Pages | : 777 |
| Release | : 2011-08-11 |
| Genre | : Mathematics |
| ISBN | : 0080475299 |
This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis.* New surveys of research problems in topology* New perspectives on classic problems* Representative surveys of research groups from all around the world
| Author | : Library of Congress |
| Publisher | : |
| Total Pages | : 954 |
| Release | : 2013 |
| Genre | : Subject headings, Library of Congress |
| ISBN | : |
| Author | : Library of Congress. Cataloging Policy and Support Office |
| Publisher | : |
| Total Pages | : 1924 |
| Release | : 2009 |
| Genre | : Subject headings, Library of Congress |
| ISBN | : |
| Author | : Csaba D. Toth |
| Publisher | : CRC Press |
| Total Pages | : 2354 |
| Release | : 2017-11-22 |
| Genre | : Computers |
| ISBN | : 1351645919 |
The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
| Author | : Peter Walters |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 472 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 0821851462 |
This volume contains the proceedings of the conference, Symbolic Dynamics and its Applications, held at Yale University in the summer of 1991 in honour of Roy L. Adler on his sixtieth birthday. The conference focused on symbolic dynamics and its applications to other fields, including: ergodic theory, smooth dynamical systems, information theory, automata theory, and statistical mechanics. Featuring a range of contributions from some of the leaders in the field, this volume presents an excellent overview of the subject.
| Author | : Shigeki Akiyama |
| Publisher | : Springer Nature |
| Total Pages | : 456 |
| Release | : 2020-12-05 |
| Genre | : Mathematics |
| ISBN | : 3030576663 |
This book presents a panorama of recent developments in the theory of tilings and related dynamical systems. It contains an expanded version of courses given in 2017 at the research school associated with the Jean-Morlet chair program. Tilings have been designed, used and studied for centuries in various contexts. This field grew significantly after the discovery of aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling problems establish a bridge between the mutually influential fields of geometry, dynamical systems, aperiodic order, computer science, number theory, algebra and logic. The main properties of tiling dynamical systems are covered, with expositions on recent results in self-similarity (and its generalizations, fusions rules and S-adic systems), algebraic developments connected to physics, games and undecidability questions, and the spectrum of substitution tilings.
