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Bifurcations Of Planar Vector Fields And Hilbert S Sixteenth Problem

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Bifurcations Of Planar Vector Fields And Hilbert S Sixteenth Problem

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Author : Robert Roussarie
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-05-19

Bifurcations Of Planar Vector Fields And Hilbert S Sixteenth Problem written by Robert Roussarie and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-19 with Mathematics categories.

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)

Bifurcations Of Planar Vector Fields And Hilbert S Sixteenth Problem

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Author : Robert Roussarie
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-26

Bifurcation Of Planar Vector Fields And Hilbert S Sixteenth Problem

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Author : Robert H. Roussarie
language : en
Publisher: Birkhauser
Release Date : 1998

Bifurcation Of Planar Vector Fields And Hilbert S Sixteenth Problem written by Robert H. Roussarie and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

Global Bifurcation Theory And Hilbert S Sixteenth Problem

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Author : V. Gaiko
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27

Global Bifurcation Theory And Hilbert S Sixteenth Problem written by V. Gaiko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.

On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk "Mathematical problems" at the Second Interna tional Congress of Mathematicians in Paris. The talk covered practically all directions of mathematical thought of that time and contained a list of 23 problems which determined the further development of mathema tics in many respects (1, 119]. Hilbert's Sixteenth Problem (the second part) was stated as follows: Problem. To find the maximum number and to determine the relative position of limit cycles of the equation dy Qn(X, y) -= dx Pn(x, y)' where Pn and Qn are polynomials of real variables x, y with real coeffi cients and not greater than n degree. The study of limit cycles is an interesting and very difficult problem of the qualitative theory of differential equations. This theory was origi nated at the end of the nineteenth century in the works of two geniuses of the world science: of the Russian mathematician A. M. Lyapunov and of the French mathematician Henri Poincare. A. M. Lyapunov set forth and solved completely in the very wide class of cases a special problem of the qualitative theory: the problem of motion stability (154]. In turn, H. Poincare stated a general problem of the qualitative analysis which was formulated as follows: not integrating the differential equation and using only the properties of its right-hand sides, to give as more as possi ble complete information on the qualitative behaviour of integral curves defined by this equation (176].

Bifurcations Of Planar Vector Fields

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Author : Freddy Dumortier
language : en
Publisher: Springer
Release Date : 2006-12-08

Bifurcations Of Planar Vector Fields written by Freddy Dumortier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.

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.

Bifurcations Of Planar Vector Fields

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Author : Jean-Pierre Francoise
language : en
Publisher: Springer
Release Date : 2006-11-14

Bifurcations Of Planar Vector Fields written by Jean-Pierre Francoise and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Concerning The Hilbert 16th Problem

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Author : S. Yakovenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

Concerning The Hilbert 16th Problem written by S. Yakovenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Differential equations categories.

Infinite Dimensional Dynamical Systems

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Author : John Mallet-Paret
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-11

Infinite Dimensional Dynamical Systems written by John Mallet-Paret and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-11 with Mathematics categories.

This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation and applications of new developments of nonlinear analysis and other mathematical theories. Theories of the infinite dimensional dynamical systems have also found more and more important applications in physical, chemical, and life sciences. This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from University of Minnesota on the occasion of his 70th birthday, this collection reflects the pioneering work and influence of Professor Sell in a few core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifolds theory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows.

Normal Forms And Bifurcation Of Planar Vector Fields

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Author : Shui-Nee Chow
language : en
Publisher: Cambridge University Press
Release Date : 1994-07-29

Normal Forms And Bifurcation Of Planar Vector Fields written by Shui-Nee Chow and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-07-29 with Mathematics categories.

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.

Planar Dynamical Systems

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Author : Yirong Liu
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-10-29

Planar Dynamical Systems written by Yirong Liu and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-29 with Mathematics categories.

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.

Bifurcations Of Planar Vector Fields And Hilbert S Sixteenth Problem

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