Concerning The Hilbert 16th Problem

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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.

Concerning The Hilbert 16th Problem

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Author : I︠U︡. S. Ilʹi︠a︡shenko
language : en
Publisher:
Release Date : 1995

Concerning The Hilbert 16th Problem written by I︠U︡. S. Ilʹi︠a︡shenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Electronic books categories.

This book examines qualitative properties of vector fields in the plane, in the spirit of Hilbert's Sixteenth Problem. Two principal topics explored are bifurcations of limit cycles of planar vector fields and desingularization of singular points for individual vector fields and for analytic families of such fields. In addition to presenting important new developments in this area, this book contains an introductory paper which outlines the general context and describes connections between the papers in the volume. The book will appeal to researchers and graduate students working in the qualit.

Nine Papers On Hilbert S 16th Problem

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Author : Dmitri_ Andreevich Gudkov G. A. Utkin
language : en
Publisher: American Mathematical Soc.
Release Date : 1978-12-31

Nine Papers On Hilbert S 16th Problem written by Dmitri_ Andreevich Gudkov G. A. Utkin 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 1978-12-31 with Mathematical analysis categories.

Translations of articles on mathematics appearing in various Russian mathematical serials.

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].

On Finiteness In Differential Equations And Diophantine Geometry

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Author : Dana Schlomiuk
language : en
Publisher: American Mathematical Soc.
Release Date :

On Finiteness In Differential Equations And Diophantine Geometry written by Dana Schlomiuk 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 with Mathematics categories.

This book focuses on finiteness conjectures and results in ordinary differential equations (ODEs) and Diophantine geometry. During the past twenty-five years, much progress has been achieved on finiteness conjectures, which are the offspring of the second part of Hilbert's 16th problem. Even in its simplest case, this is one of the very few problems on Hilbert's list which remains unsolved. These results are about existence and estimation of finite bounds for the number of limit cycles occurring in certain families of ODEs. The book describes this progress, the methods used (bifurcation theory, asymptotic expansions, methods of differential algebra, or geometry) and the specific results obtained. The finiteness conjectures on limit cycles are part of a larger picture that also includes finiteness problems in other areas of mathematics, in particular those in Diophantine geometry where remarkable results were proved during the same period of time. There is a chapter devoted to finiteness results in D The volume can be used as an independent study text for advanced undergraduates and graduate students studying ODEs or applications of differential algebra to differential equations and Diophantine geometry. It is also is a good entry point for researchers interested these areas, in particular, in limit cycles of ODEs, and in finiteness problems. Contributors to the volume include Andrey Bolibrukh and Alexandru Buium. Available from the AMS by A. Buium is Arithmetic Differential Equations, as Volume 118 in the Mathematical Surveys and Monographs series.

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

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 2013-11-26 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)

Hilbet S 16th Problem

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Author : Courtney S. Coleman
language : en
Publisher:
Release Date : 1976

Hilbet S 16th Problem written by Courtney S. Coleman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Biological rhythms categories.

The Stokes Phenomenon And Hilbert S 16th Problem

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Author : B L J Braaksma
language : en
Publisher: World Scientific
Release Date : 1996-05-06

The Stokes Phenomenon And Hilbert S 16th Problem written by B L J Braaksma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-06 with categories.

The 16th Problem of Hilbert is one of the most famous remaining unsolved problems of mathematics. It concerns whether a polynomial vector field on the plane has a finite number of limit cycles. There is a strong connection with divergent solutions of differential equations, where a central role is played by the Stokes Phenomenon, the change in asymptotic behaviour of the solutions in different sectors of the complex plane.The contributions to these proceedings survey both of these themes, including historical and modern theoretical points of view. Topics covered include the Riemann-Hilbert problem, Painleve equations, nonlinear Stokes phenomena, and the inverse Galois problem.

Arnold S Problems

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Author : Vladimir I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-24

Arnold S Problems written by Vladimir I. Arnold 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 2004-06-24 with Mathematics categories.

Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research

Normal Forms Bifurcations And Finiteness Problems In Differential Equations

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Author : Christiane Rousseau
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-02-29

Normal Forms Bifurcations And Finiteness Problems In Differential Equations written by Christiane Rousseau 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 2004-02-29 with Mathematics categories.

Proceedings of the Nato Advanced Study Institute, held in Montreal, Canada, from 8 to 19 July 2002