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Author : A. Vanderbauwhede
Publisher :
ISBN 13 :
Total Pages : 368 pages
Book Rating : 4.3/5 (91 download)
Download or read book Local Bifurcation and Symmetry written by A. Vanderbauwhede and published by . This book was released on 1982 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bernold Fiedler
Publisher : Springer
ISBN 13 : 3540391509
Total Pages : 151 pages
Book Rating : 4.5/5 (43 download)
Download or read book Global Bifurcation of Periodic Solutions with Symmetry written by Bernold Fiedler and published by Springer. This book was released on 2006-11-14 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This largely self-contained research monograph addresses the following type of questions. Suppose one encounters a continuous time dynamical system with some built-in symmetry. Should one expect periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? Probing into these questions leads from dynamics to topology, algebra, singularity theory, and to many applications. Within a global approach, the emphasis is on periodic motions far from equilibrium. Mathematical methods include bifurcation theory, transversality theory, and generic approximations. A new homotopy invariant is designed to study the global interdependence of symmetric periodic motions. Besides mathematical techniques, the book contains 5 largely nontechnical chapters. The first three outline the main questions, results and methods. A detailed discussion pursues theoretical consequences and open problems. Results are illustrated by a variety of applications including coupled oscillators and rotating waves: these links to such disciplines as theoretical biology, chemistry, fluid dynamics, physics and their engineering counterparts make the book directly accessible to a wider audience.
Author : André L. Vanderbauwhede
Publisher :
ISBN 13 :
Total Pages : 318 pages
Book Rating : 4.:/5 (897 download)
Download or read book Local bifurcation and symmetry written by André L. Vanderbauwhede and published by . This book was released on 1980 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jorge Buescu
Publisher : Birkhäuser
ISBN 13 : 3034879822
Total Pages : 215 pages
Book Rating : 4.0/5 (348 download)
Download or read book Bifurcation, Symmetry and Patterns written by Jorge Buescu and published by Birkhäuser. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest developments on both the theory and applications of bifurcations with symmetry. The text includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the work of Martin Golubitsky and Ian Stewart and its influence in modern mathematics at the same time as it contains work of young mathematicians in new directions. The range of topics includes mathematical biology, pattern formation, ergodic theory, normal forms, one-dimensional dynamics and symmetric dynamics.
Author : BÖHMER
Publisher : Birkhäuser
ISBN 13 : 3034875363
Total Pages : 323 pages
Book Rating : 4.0/5 (348 download)
Download or read book Bifurcation and Symmetry written by BÖHMER and published by Birkhäuser. This book was released on 2013-03-08 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry is a property which occurs throughout nature and it is therefore natural that symmetry should be considered when attempting to model nature. In many cases, these models are also nonlinear and it is the study of nonlinear symmetric models that has been the basis of much recent work. Although systematic studies of nonlinear problems may be traced back at least to the pioneering contributions of Poincare, this remains an area with challenging problems for mathematicians and scientists. Phenomena whose models exhibit both symmetry and nonlinearity lead to problems which are challenging and rich in complexity, beauty and utility. In recent years, the tools provided by group theory and representation theory have proven to be highly effective in treating nonlinear problems involving symmetry. By these means, highly complex situations may be decomposed into a number of simpler ones which are already understood or are at least easier to handle. In the realm of numerical approximations, the systematic exploitation of symmetry via group repre sentation theory is even more recent. In the hope of stimulating interaction and acquaintance with results and problems in the various fields of applications, bifurcation theory and numerical analysis, we organized the conference and workshop Bifurcation and Symmetry: Cross Influences between Mathematics and Applications during June 2-7,8-14, 1991 at the Philipps University of Marburg, Germany.
Author : Pascal Chossat
Publisher : Springer Science & Business Media
ISBN 13 :
Total Pages : 380 pages
Book Rating : 4.3/5 (91 download)
Download or read book Dynamics, Bifurcation, and Symmetry written by Pascal Chossat and published by Springer Science & Business Media. This book was released on 1994 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summarizes the work of the European Bifurcation Theory Group after its first two years. The 28 papers discuss oscillator networks with the symmetry of the unit quaternion group, non- linear parabolic evolutions in unbounded domains, and symmetries and reversing symmetries in kicked systems. No index. Annotation copyright by Book News, Inc., Portland, OR
Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
ISBN 13 : 1475739788
Total Pages : 648 pages
Book Rating : 4.4/5 (757 download)
Download or read book Elements of Applied Bifurcation Theory written by Yuri Kuznetsov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.
Author : Werner Dubitzky
Publisher : Springer
ISBN 13 : 9781441998620
Total Pages : 0 pages
Book Rating : 4.9/5 (986 download)
Download or read book Encyclopedia of Systems Biology written by Werner Dubitzky and published by Springer. This book was released on 2013-06-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems biology refers to the quantitative analysis of the dynamic interactions among several components of a biological system and aims to understand the behavior of the system as a whole. Systems biology involves the development and application of systems theory concepts for the study of complex biological systems through iteration over mathematical modeling, computational simulation and biological experimentation. Systems biology could be viewed as a tool to increase our understanding of biological systems, to develop more directed experiments, and to allow accurate predictions. The Encyclopedia of Systems Biology is conceived as a comprehensive reference work covering all aspects of systems biology, in particular the investigation of living matter involving a tight coupling of biological experimentation, mathematical modeling and computational analysis and simulation. The main goal of the Encyclopedia is to provide a complete reference of established knowledge in systems biology – a ‘one-stop shop’ for someone seeking information on key concepts of systems biology. As a result, the Encyclopedia comprises a broad range of topics relevant in the context of systems biology. The audience targeted by the Encyclopedia includes researchers, developers, teachers, students and practitioners who are interested or working in the field of systems biology. Keeping in mind the varying needs of the potential readership, we have structured and presented the content in a way that is accessible to readers from wide range of backgrounds. In contrast to encyclopedic online resources, which often rely on the general public to author their content, a key consideration in the development of the Encyclopedia of Systems Biology was to have subject matter experts define the concepts and subjects of systems biology.
Author : Mariana Haragus
Publisher : Springer Science & Business Media
ISBN 13 : 0857291122
Total Pages : 338 pages
Book Rating : 4.8/5 (572 download)
Download or read book Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems written by Mariana Haragus and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.
Author : Pascal Chossat
Publisher : Springer Science & Business Media
ISBN 13 : 9401109567
Total Pages : 355 pages
Book Rating : 4.4/5 (11 download)
Download or read book Dynamics, Bifurcation and Symmetry written by Pascal Chossat and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects contributions to the conference" Dynamics, Bifurcation and Symmetry, new trends and new tools", which was held at the Institut d'Etudes Sci entifiques de Cargese (France), September 3-9, 1993. The first aim of this conference was to gather and summarize the work of the European Bifurcation Theory Group after two years of existence (the EBTG links european laboratories in five countries via an EC grant). Thanks to a NATO ARW grant, the conference developed into an international meeting on bifurcation theory and dynamical systems, with the partic ipation of leading specialists not only from Europe but also from overseas countries (Canada, USA, South America). It was a great satisfaction to notice the active, and quite enthusiastic participation of many young scientists. This is reflected in the present book for which many contributors are PhD students or post-doc researchers. Although several "big" themes (bifurcation with symmetry, low dimensional dynam ics, dynamics in EDP's, applications, . . . ) are present in these proceedings, we have divided the book into corresponding parts. In fact these themes overlap in most contributions, which seems to reflect a general tendancy in nonlinear science. I am very pleased to thank for their support the NATO International Exchange Scientific Program as well as the EEC Science Program, which made possible the suc cess of this conference.
Author :
Publisher :
ISBN 13 : 9780387192345
Total Pages : 144 pages
Book Rating : 4.1/5 (923 download)
Download or read book Global Bifurcation of Periodic Solutions with Symmetry written by and published by . This book was released on 1988 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael J Field
Publisher : World Scientific
ISBN 13 : 1908979178
Total Pages : 492 pages
Book Rating : 4.9/5 (89 download)
Download or read book Dynamics and Symmetry written by Michael J Field and published by World Scientific. This book was released on 2007-09-03 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the first systematic exposition of the global and local theory of dynamics equivariant with respect to a (compact) Lie group. Aside from general genericity and normal form theorems on equivariant bifurcation, it describes many general families of examples of equivariant bifurcation and includes a number of novel geometric techniques, in particular, equivariant transversality. This important book forms a theoretical basis of future work on equivariant reversible and Hamiltonian systems. This book also provides a general and comprehensive introduction to codimension one equivariant bifurcation theory. In particular, it includes the bifurcation theory developed with Roger Richardson on subgroups of reflection groups and the Maximal Isotropy Subgroup Conjecture. A number of general results are also given on the global theory. Introductory material on groups, representations and G-manifolds are covered in the first three chapters of the book. In addition, a self-contained introduction of equivariant transversality is given, including necessary results on stratifications as well as results on equivariant jet transversality developed by Edward Bierstone. Contents:GroupsGroup Actions and RepresentationsSmooth G-manifoldsEquivariant Bifurcation Theory: Steady State BifurcationEquivariant Bifurcation Theory: DynamicsEquivariant TransversalityApplications of G-transversality to Bifurcation Theory IEquivariant DynamicsDynamical Systems on G-manifoldsApplications of G-transversality to Bifurcation Theory II Readership: Academics and graduate students in pure and applied mathematics. Keywords:Dynamics;Symmetry;Bifurcation;Equivariant Maps;Equivariant Transversality;Homoclinic Cycle;Relative Equilibrium;Compact Lie Group;Determinacy;Symmetric AttractorsKey Features:First comprehensive book on equivariant transversalityPresents general theories of equivariant steady state and Hopf bifurcation, including rather new results on bifurcation from relative equilibria and relative periodic orbitsContains sections on equivariant reversible systemsIntroduces a range of new geometric tools for the study of steady state and Hopf bifurcationIncludes exercises with many recent and useful examples given
Author : Shangjiang Guo
Publisher : Springer Science & Business Media
ISBN 13 : 1461469929
Total Pages : 295 pages
Book Rating : 4.4/5 (614 download)
Download or read book Bifurcation Theory of Functional Differential Equations written by Shangjiang Guo and published by Springer Science & Business Media. This book was released on 2013-07-30 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).
Author : David H. Sattinger
Publisher : SIAM
ISBN 13 : 9781611970296
Total Pages : 80 pages
Book Rating : 4.9/5 (72 download)
Download or read book Branching in the Presence of Symmetry written by David H. Sattinger and published by SIAM. This book was released on 1983-01-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of developments in the field of bifurcation theory, with emphasis on symmetry breaking and its interrelationship with singularity theory. The notions of universal solutions, symmetry breaking, and unfolding of singularities are discussed in detail. The book not only reviews recent mathematical developments but also provides a stimulus for further research in the field.
Author : Heinz Hanßmann
Publisher : Springer
ISBN 13 : 3540388966
Total Pages : 248 pages
Book Rating : 4.5/5 (43 download)
Download or read book Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems written by Heinz Hanßmann and published by Springer. This book was released on 2006-10-18 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.
Author : Philip Holmes
Publisher : Cambridge University Press
ISBN 13 : 1107008255
Total Pages : 403 pages
Book Rating : 4.1/5 (7 download)
Download or read book Turbulence, Coherent Structures, Dynamical Systems and Symmetry written by Philip Holmes and published by Cambridge University Press. This book was released on 2012-02-23 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.
Author : Gérard Iooss
Publisher : World Scientific Publishing Company
ISBN 13 : 9813105348
Total Pages : 196 pages
Book Rating : 4.8/5 (131 download)
Download or read book Topics in Bifurcation Theory and Applications written by Gérard Iooss and published by World Scientific Publishing Company. This book was released on 1999-01-22 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the most efficient analytical techniques in the local bifurcation theory of vector fields. It is centered on the theory of normal forms and its applications, including interaction with symmetries. The first part of the book reviews the center manifold reduction and introduces normal forms (with complete proofs). Basic bifurcations are studied together with bifurcations in the presence of symmetries. Special attention is given to examples with reversible vector fields, including the physical example given by the water waves. In this second edition, many problems with detailed solutions are added at the end of the first part (some systems being in infinite dimensions). The second part deals with the Couette–Taylor hydrodynamical stability problem, between concentric rotating cylinders. The spatial structure of various steady or unsteady solutions results directly from the analysis of the reduced system on a center manifold. In this part we also study bifurcations (simple here) from group orbits of solutions in an elementary way (avoiding heavy algebra). The third part analyzes bifurcations from time periodic solutions of autonomous vector fields. A normal form theory is developed, covering all cases, and emphasizing a partial Floquet reduction theory, which is applicable in infinite dimensions. Studies of period doubling as well as Arnold's resonance tongues are included in this part.
