Download or read book Bifurcations of Planar Vector Fields written by Freddy Dumortier and published by Springer. This book was released on 2006-12-08 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Bifurcations of Planar Vector Fields written by Jean-Pierre Francoise and published by . This book was released on 2014-01-15 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bifurcations of Planar Vector Fields written by Jean-Pierre Francoise and published by Springer. This book was released on 2006-11-14 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Normal Forms and Bifurcation of Planar Vector Fields written by Shui-Nee Chow and published by Cambridge University Press. This book was released on 1994-07-29 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Bifurcations of Planar Vector Fields and Hilbert s Sixteenth Problem written by Robert Roussarie and published by Springer Science & Business Media. This book was released on 1998-05-19 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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)
Download or read book Bifurcations of Planar Vector Fields and Hilbert s Sixteenth Problem written by Robert Roussarie and published by Springer Science & Business Media. This book was released on 2013-11-26 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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)
Download or read book Bifurcations of planar vector fields and Hilbert s 16th problem written by Robert H. Roussarie and published by . This book was released on 1995 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bifurcations and Periodic Orbits of Vector Fields written by Dana Schlomiuk and published by Springer Science & Business Media. This book was released on 1993-07-31 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Bifurcations and Periodic Orbits of Vector Fields written by Dana Schlomiuk and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Bifurcation of Planar Vector Fields and Hilbert s Sixteenth Problem written by Robert H. Roussarie and published by Birkhauser. This book was released on 1998 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Investigation of Global Bifurcations in Planar Vector Fields written by John Guckenheimer and published by . This book was released on 1988 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Bifurcation of Symmetric Planar Vector Fields written by Hyeong-Kwan Ju and published by . This book was released on 1988 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rigorous Computer Verification of Planar Vector Field Structure written by Salvador Malo and published by . This book was released on 1994 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Planar Dynamical Systems written by Yirong Liu and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-10-29 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert’s 16th problem. These problems had been posed more than 110 years ago. Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert’s 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.
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.
Download or read book Bifurcations of Planar Vector Fields and Hilbert s 16th Problem written by Robert H. Roussarie and published by . This book was released on 1995* with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Desingularization of Nilpotent Singularities in Families of Planar Vector Fields written by Daniel Panazzolo and published by American Mathematical Soc.. This book was released on 2002 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work aims to prove a desingularization theorem for analytic families of two-dimensional vector fields, under the hypothesis that all its singularities have a non-vanishing first jet. Application to problems of singular perturbations and finite cyclicity are discussed in the last chapter.
