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Outer Billiards On Kites
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Book Synopsis Outer Billiards on Kites by : Richard Evan Schwartz
Download or read book Outer Billiards on Kites written by Richard Evan Schwartz and published by Princeton University Press. This book was released on 2009-10-05 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks whether or not one can have an outer billiards system with an unbounded orbit. The Moser-Neumann question is an idealized version of the question of whether, because of small disturbances in its orbit, the Earth can break out of its orbit and fly away from the Sun. In Outer Billiards on Kites, Richard Schwartz presents his affirmative solution to the Moser-Neumann problem. He shows that an outer billiards system can have an unbounded orbit when defined relative to any irrational kite. A kite is a quadrilateral having a diagonal that is a line of bilateral symmetry. The kite is irrational if the other diagonal divides the quadrilateral into two triangles whose areas are not rationally related. In addition to solving the basic problem, Schwartz relates outer billiards on kites to such topics as Diophantine approximation, the modular group, self-similar sets, polytope exchange maps, profinite completions of the integers, and solenoids--connections that together allow for a fairly complete analysis of the dynamical system.
Book Synopsis The Plaid Model by : Richard Evan Schwartz
Download or read book The Plaid Model written by Richard Evan Schwartz and published by Princeton University Press. This book was released on 2019-02-19 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. The Plaid Model, which is a self-contained sequel to Richard Schwartz’s Outer Billiards on Kites, provides a combinatorial model for orbits of outer billiards on kites. Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called “the plaid model,” has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics. The book includes an extensive computer program that allows readers to explore the materials interactively and each theorem is accompanied by a computer demonstration.
Book Synopsis XVIIth International Congress on Mathematical Physics by : Arne Jensen
Download or read book XVIIth International Congress on Mathematical Physics written by Arne Jensen and published by World Scientific. This book was released on 2014 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an in-depth study of not just about Tan Kah-kee, but also the making of a legend through his deeds, self-sacrifices, fortitude and foresight. This revised edition sheds new light on his political agonies in Mao's China over campaigns against capitalists and intellectuals.
Book Synopsis Annals of Mathematics Studies by : Richard Evan Schwartz
Download or read book Annals of Mathematics Studies written by Richard Evan Schwartz and published by . This book was released on 1940 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks whether or not one can have an outer billiards system with an unbounded orbit. The Moser-Neumann question is an idealized version of the question of whether, because of small disturbances in its orbit, the Earth can break out of its orbit and fly away from the Sun. In Outer Billiards on Kites, Richard Schwartz presents his affirmative solution to the Moser-Neumann problem. He shows that an outer billiards system can have an unbounded orbit when defined relative to any irrational kite. A kite is a quadrilateral having a diagonal that is a line of bilateral symmetry. The kite is irrational if the other diagonal divides the quadrilateral into two triangles whose areas are not rationally related. In addition to solving the basic problem, Schwartz relates outer billiards on kites to such topics as Diophantine approximation, the modular group, self-similar sets, polytope exchange maps, profinite completions of the integers, and solenoids--connections that together allow for a fairly complete analysis of the dynamical system."--Publisher website.
Book Synopsis Geometric and Probabilistic Structures in Dynamics by : Keith Burns
Download or read book Geometric and Probabilistic Structures in Dynamics written by Keith Burns and published by American Mathematical Soc.. This book was released on 2008 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents a collection of articles that cover areas of mathematics related to dynamical systems. The authors are well-known experts who use geometric and probabilistic methods to study interesting problems in the theory of dynamical systems and its applications. Some of the articles are surveys while others are original contributions. The topics covered include: Riemannian geometry, models in mathematical physics and mathematical biology, symbolic dynamics, random and stochastic dynamics. This book can be used by graduate students and researchers in dynamical systems and its applications."--BOOK JACKET.
Book Synopsis Dear Professor Dyson by : Freeman John Dyson
Download or read book Dear Professor Dyson written by Freeman John Dyson and published by World Scientific. This book was released on 2016 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Freeman Dyson has designed nuclear reactors and bomb-powered spacecraft; he has studied the origins of life and the possibilities for the long-term future; he showed quantum mechanics to be consistent with electrodynamics and started cosmological eschatology; he has won international recognition for his work in science and for his work in reconciling science to religion; he has advised generals and congressional committees. An STS (Science, Technology, Society) curriculum or discussion group that engages topics such as nuclear policies, genetic technologies, environmental sustainability, the role of religion in a scientific society, and a hard look towards the future, would count itself privileged to include Professor Dyson as a class participant and mentor. In this book, STS topics are not discussed as objectified abstractions, but through personal stories. The reader is invited to observe Dyson's influence on a generation of young people as they wrestle with issues of science, technology, society, life in general and our place in the universe. The book is filled with personal anecdotes, student questions and responses, honest doubts and passions"--
Book Synopsis Peregrinations From Physics To Phylogeny: Essays On The Occasion Of Hao Bailin's 80th Birthday by : Kok Khoo Phua
Download or read book Peregrinations From Physics To Phylogeny: Essays On The Occasion Of Hao Bailin's 80th Birthday written by Kok Khoo Phua and published by World Scientific. This book was released on 2016-02-29 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Professor Hao Bailin is one of China's most talented and most versatile theoretical physicists. He has made important contributions to a wide variety of research fields, including biology in which he pioneered a multidimensional method for studying the evolutionary pathways of bacteria. Indeed he calls himself, appreciatively I believe, a guerrilla fighter.'Chen-Ning Yang, Nobel Laureate
Book Synopsis Mathematical Writing by : Franco Vivaldi
Download or read book Mathematical Writing written by Franco Vivaldi and published by Springer. This book was released on 2014-11-04 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition. Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150 of them have complete solutions, to facilitate self-study. Mathematical Writing will be of interest to all mathematics students who want to raise the quality of their coursework, reports, exams, and dissertations.
Book Synopsis In the Tradition of Ahlfors-Bers, V by : Mario Bonk
Download or read book In the Tradition of Ahlfors-Bers, V written by Mario Bonk and published by American Mathematical Soc.. This book was released on 2010 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Ahlfors-Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this legacy lies in the fields of geometric function theory, Teichmuller theory, hyperbolic geometry, and partial differential equations. However, the work of Ahlfors and Bers has impacted and created interactions with many other fields of mathematics, such as algebraic geometry, dynamical systems, topology, geometric group theory, mathematical physics, and number theory. Recent years have seen a flowering of this legacy with an increased interest in their work. This current volume contains articles on a wide variety of subjects that are central to this legacy. These include papers in Kleinian groups, classical Riemann surface theory, translation surfaces, algebraic geometry and dynamics. The majority of the papers present new research, but there are survey articles as well.
Book Synopsis The Octagonal PETs by : Richard Evan Schwartz
Download or read book The Octagonal PETs written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2014-07-03 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: A polytope exchange transformation is a (discontinuous) map from a polytope to itself that is a translation wherever it is defined. The 1-dimensional examples, interval exchange transformations, have been studied fruitfully for many years and have deep connections to other areas of mathematics, such as Teichmüller theory. This book introduces a general method for constructing polytope exchange transformations in higher dimensions and then studies the simplest example of the construction in detail. The simplest case is a 1-parameter family of polygon exchange transformations that turns out to be closely related to outer billiards on semi-regular octagons. The 1-parameter family admits a complete renormalization scheme, and this structure allows for a fairly complete analysis both of the system and of outer billiards on semi-regular octagons. The material in this book was discovered through computer experimentation. On the other hand, the proofs are traditional, except for a few rigorous computer-assisted calculations.
Book Synopsis What's Happening in the Mathematical Sciences by : Dana Mackenzie
Download or read book What's Happening in the Mathematical Sciences written by Dana Mackenzie and published by American Mathematical Soc.. This book was released on 2010-12-29 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume showcases the latest remarkable progress in pure and applied mathematics, written in an engaging style that conveys modern mathematics' thrill of discovery. Among the stories in this volume are several showing mathematics' significant role in current events, from the financial crisis to breast cancer screening. The book chronicles several important conjectures that mathematicians have settled in the past several years.
Book Synopsis Science by : John Michels (Journalist)
Download or read book Science written by John Michels (Journalist) and published by . This book was released on 2007 with total page 1000 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Ergodic Theory of Lattice Subgroups by : Alexander Gorodnik
Download or read book The Ergodic Theory of Lattice Subgroups written by Alexander Gorodnik and published by . This book was released on 1940 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convolution and Equidistribution by : Nicholas M. Katz
Download or read book Convolution and Equidistribution written by Nicholas M. Katz and published by . This book was released on 1940 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Some Problems of Unlikely Intersections in Arithmetic and Geometry by : Umberto Zannier
Download or read book Some Problems of Unlikely Intersections in Arithmetic and Geometry written by Umberto Zannier and published by . This book was released on 1940 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Decomposition of Global Conformal Invariants by : Spyros Alexakis
Download or read book The Decomposition of Global Conformal Invariants written by Spyros Alexakis and published by . This book was released on 1940 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces by : Joram Lindenstrauss
Download or read book Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces written by Joram Lindenstrauss and published by . This book was released on 1940 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
