Download or read book Knots and Links in Three Dimensional Flows written by Robert W. Ghrist and published by Springer. This book was released on 2006-11-14 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The closed orbits of three-dimensional flows form knots and links. This book develops the tools - template theory and symbolic dynamics - needed for studying knotted orbits. This theory is applied to the problems of understanding local and global bifurcations, as well as the embedding data of orbits in Morse-smale, Smale, and integrable Hamiltonian flows. The necesssary background theory is sketched; however, some familiarity with low-dimensional topology and differential equations is assumed.
Download or read book Knots and Links in Three Dimensional Flows written by Robert W. Ghrist and published by . This book was released on 2014-09-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Three Dimensional Flows written by Vítor Araújo and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Knots Links Braids and 3 Manifolds written by Viktor Vasilʹevich Prasolov and published by American Mathematical Soc.. This book was released on 1997 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.
Download or read book Three Dimensional Flows written by and published by . This book was released on 2007 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Knots in Hellas 98 Proceedings of the International Conference on Knot Theory and Its Ramifications written by V. F. R. Jones and published by World Scientific. This book was released on 2000 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: There have been exciting developments in the area of knot theory in recent years. They include Thurston's work on geometric structures on 3-manifolds (e.g. knot complements), Gordon–Luecke work on surgeries on knots, Jones' work on invariants of links in S3, and advances in the theory of invariants of 3-manifolds based on Jones- and Vassiliev-type invariants of links. Jones ideas and Thurston's idea are connected by the following path: hyperbolic structures, PSL(2, C) representations, character varieties, quantization of the coordinate ring of the variety to skein modules (i.e. Kauffman, bracket skein module), and finally quantum invariants of 3-manifolds. This proceedings volume covers all those exciting topics.
Download or read book The N Vortex Problem written by Paul K. Newton and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to current research on the N- vortex problem of fluid mechanics. It describes the Hamiltonian aspects of vortex dynamics as an entry point into the rather large literature on the topic, with exercises at the end of each chapter.
Download or read book Robust Chaos and Its Applications written by Elhadj Zeraoulia and published by World Scientific. This book was released on 2012 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.
Download or read book The Topology of Chaos written by Robert Gilmore and published by John Wiley & Sons. This book was released on 2012-04-30 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems. The authors provide a deep understanding of the structure of strange attractors, how they are classified, and how the information required to identify and classify a strange attractor can be extracted from experimental data. In its first edition, the Topology of Chaos has been a valuable resource for physicist and mathematicians interested in the topological analysis of dynamical systems. Since its publication in 2002, important theoretical and experimental advances have put the topological analysis program on a firmer basis. This second edition includes relevant results and connects the material to other recent developments. Following significant improvements will be included: * A gentler introduction to the topological analysis of chaotic systems for the non expert which introduces the problems and questions that one commonly encounters when observing a chaotic dynamics and which are well addressed by a topological approach: existence of unstable periodic orbits, bifurcation sequences, multistability etc. * A new chapter is devoted to bounding tori which are essential for achieving generality as well as for understanding the influence of boundary conditions. * The new edition also reflects the progress which had been made towards extending topological analysis to higher-dimensional systems by proposing a new formalism where evolving triangulations replace braids. * There has also been much progress in the understanding of what is a good representation of a chaotic system, and therefore a new chapter is devoted to embeddings. * The chapter on topological analysis program will be expanded to cover traditional measures of chaos. This will help to connect those readers who are familiar with those measures and tests to the more sophisticated methodologies discussed in detail in this book. * The addition of the Appendix with both frequently asked and open questions with answers gathers the most essential points readers should keep in mind and guides to corresponding sections in the book. This will be of great help to those who want to selectively dive into the book and its treatments rather than reading it cover to cover. What makes this book special is its attempt to classify real physical systems (e.g. lasers) using topological techniques applied to real date (e.g. time series). Hence it has become the experimenter?s guidebook to reliable and sophisticated studies of experimental data for comparison with candidate relevant theoretical models, inevitable to physicists, mathematicians, and engineers studying low-dimensional chaotic systems.
Download or read book Handbook of Dynamical Systems written by H. Broer and published by Elsevier. This book was released on 2010-11-10 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. - Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems - Highlights developments that are the foundation for future research in this field - Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems
Download or read book Dynamical Systems written by Zeraoulia Elhadj and published by CRC Press. This book was released on 2019-01-21 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos is the idea that a system will produce very different long-term behaviors when the initial conditions are perturbed only slightly. Chaos is used for novel, time- or energy-critical interdisciplinary applications. Examples include high-performance circuits and devices, liquid mixing, chemical reactions, biological systems, crisis management, secure information processing, and critical decision-making in politics, economics, as well as military applications, etc. This book presents the latest investigations in the theory of chaotic systems and their dynamics. The book covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. This book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems.
Download or read book Classifying Knots and Links in L 1 1 Template written by H. B. M. K. Hiroshani Senarathna and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A template is a key tool that we use to study knotted periodic orbits in the three-dimensional flow. The simplest type of template is the Lorenz template. In [5], Birman and Williams studied knotted periodic orbits with aid of the Lorenz template. They discovered remarkable properties of Lorenz knots and links. No half twists exist in the Lorenz template. The new template is referred to be a Lorenz-like template when we add half twists. We looked at the template L(1, −1) in this paper, which has a positive half twist on the left-side and a negative half twist on the right. We look for the different types of knots and links that the template contains. Afterward, it was discovered that some knot types in L(1, −1) are fibered. Additionally, we look into the linking number of links in L(1, −1), as well as L(m, n) for m > 0 and n
Download or read book Encyclopedia of Nonlinear Science written by Alwyn Scott and published by Routledge. This book was released on 2006-05-17 with total page 2881 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.
Download or read book Introduction to Applied Nonlinear Dynamical Systems and Chaos written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik
Download or read book Physics and Theoretical Computer Science written by Jean-Pierre Gazeau and published by IOS Press. This book was released on 2007 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to reinforce the interface between physical sciences, theoretical computer science, and discrete mathematics. This book assembles theoretical physicists and specialists of theoretical informatics and discrete mathematics in order to learn about developments in cryptography, algorithmics, and more.
Download or read book The Scientific Legacy of Poincare written by Éric Charpentier and published by American Mathematical Soc.. This book was released on 2010 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Henri Poincare (1854-1912) was one of the greatest scientists of his time, perhaps the last one to have mastered and expanded almost all areas in mathematics and theoretical physics. In this book, twenty world experts present one part of Poincare's extraordinary work. Each chapter treats one theme, presenting Poincare's approach, and achievements.
