Bifurcation of Symmetric Planar Vector Fields PDF Download

Author: Hyeong-Kwan Ju
Publisher:
ISBN:
Category : Bifurcation theory
Languages : en
Pages : 324

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Author: Shui-Nee Chow
Publisher: Cambridge University Press
ISBN: 0521372267
Category : Mathematics
Languages : en
Pages : 482

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Book Description
This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary.

Author: Freddy Dumortier
Publisher: Springer
ISBN: 3540384332
Category : Mathematics
Languages : en
Pages : 234

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Book Description
The book reports on recent work by the authors on the bifurcation structure of singular points of planar vector fields whose linear parts are nilpotent. The bifurcation diagrams of the most important codimension-three cases are studied in detail. The results presented reach the limits of what is currently known on the bifurcation theory of planar vector fields. While the treatment is geometric, special analytical tools using abelian integrals are needed, and are explicitly developed. The rescaling and normalization methods are improved for application here. The reader is assumed to be familiar with the elements of Bifurcation and Dynamical Systems Theory. The book is addressed to researchers and graduate students working in Ordinary Differential Equations and Dynamical Systems, as well as anyone modelling complex multiparametric phenomena.

Author: Jean-Pierre Francoise
Publisher: Springer
ISBN: 354046722X
Category : Mathematics
Languages : en
Pages : 404

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Author: Robert Roussarie
Publisher: Springer Science & Business Media
ISBN: 303480718X
Category : Mathematics
Languages : en
Pages : 215

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Book Description
In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets. The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations. - - - The book as a whole is a well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in the recently developed methods. The book, reflecting the current state of the art, can also be used for teaching special courses. (Mathematical Reviews)

Author: John Guckenheimer
Publisher:
ISBN:
Category :
Languages : en
Pages : 4

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Book Description
The general area of the research has been the investigation of nonlinear dynamical systems and their bifurcations . A number of different investigations of bifurcation in multiparameter systems of differential equations have been undertaken. (1) The investigation of global bifurcations in planar vector fields: In studying higher codimension bifurcations in models of chemical reactors, it was necessary to study codimension two bifurcations involving the presence of homoclinic orbits for these systems. A classification of codimension two bifurcations involving a single saddle point was constructed and applied to chemical reactor problems. (2) The investigation of dynamical systems with symmetry groups: A significant discovery is the occurrence of heteroclinic cycles that are structurally stable within the class of symmetric systems. (3) The investigation of one dimensional mappings; Attracting Cantor sets that occur at the limit of period doubling sequences of bifurcations have Lebesgue measure zero. (jhd).

Author: Pascal Chossat
Publisher: Springer Science & Business Media
ISBN: 9401109567
Category : Mathematics
Languages : en
Pages : 355

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Book Description
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: John Guckenheimer
Publisher: Springer Science & Business Media
ISBN: 1461211409
Category : Mathematics
Languages : en
Pages : 475

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Book Description
An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Author: G‚rard Iooss
Publisher: World Scientific
ISBN: 9789810237288
Category : Technology & Engineering
Languages : en
Pages : 204

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Book Description
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.

Author: Dana Schlomiuk
Publisher: Springer Science & Business Media
ISBN: 9401582386
Category : Mathematics
Languages : en
Pages : 483

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Book Description
The last thirty years were a period of continuous and intense growth in the subject of dynamical systems. New concepts and techniques and at the same time new areas of applications of the theory were found. The 31st session of the Seminaire de Mathematiques Superieures (SMS) held at the Universite de Montreal in July 1992 was on dynamical systems having as its center theme "Bifurcations and periodic orbits of vector fields". This session of the SMS was a NATO Advanced Study Institute (ASI). This ASI had the purpose of acquainting the participants with some of the most recent developments and of stimulating new research around the chosen center theme. These developments include the major tools of the new resummation techniques with applications, in particular to the proof of the non-accumulation of limit-cycles for real-analytic plane vector fields. One of the aims of the ASI was to bring together methods from real and complex dy namical systems. There is a growing awareness that an interplay between real and complex methods is both useful and necessary for the solution of some of the problems. Complex techniques become powerful tools which yield valuable information when applied to the study of the dynamics of real vector fields. The recent developments show that no rigid frontiers between disciplines exist and that interesting new developments occur when ideas and techniques from diverse disciplines are married. One of the aims of the ASI was to show these multiple interactions at work.