Bifurcations Of Planar Vector Fields And Hilbert S 16th 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 : 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)
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.
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.
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.
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].
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.
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.
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
Nostradamus 2013 Prediction Modeling And Analysis Of Complex Systems
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Author : Ivan Zelinka
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-13
Nostradamus 2013 Prediction Modeling And Analysis Of Complex Systems written by Ivan Zelinka 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 2013-11-13 with Technology & Engineering categories.
Prediction of behavior of the dynamical systems, analysis and modeling of its structure is vitally important problem in engineering, economy and science today. Examples of such systems can be seen in the world around us and of course in almost every scientific discipline including such “exotic” domains like the earth’s atmosphere, turbulent fluids, economies (exchange rate and stock markets), population growth, physics (control of plasma), information flow in social networks and its dynamics, chemistry and complex networks. To understand such dynamics and to use it in research or industrial applications, it is important to create its models. For this purpose there is rich spectra of methods, from classical like ARMA models or Box Jenkins method to such modern ones like evolutionary computation, neural networks, fuzzy logic, fractal geometry, deterministic chaos and more. This proceeding book is a collection of the accepted papers to conference Nostradamus that has been held in Ostrava, Czech Republic. Proceeding also comprises of outstanding keynote speeches by distinguished guest speakers: Guanrong Chen (Hong Kong), Miguel A. F. Sanjuan (Spain), Gennady Leonov and Nikolay Kuznetsov (Russia), Petr Škoda (Czech Republic). The main aim of the conference is to create periodical possibility for students, academics and researchers to exchange their ideas and novel methods. This conference will establish forum for presentation and discussion of recent trends in the area of applications of various predictive methods for researchers, students and academics.
Progress In Analysis Proceedings Of The 3rd Isaac Congress In 2 Volumes
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Author : Heinrich G W Begehr
language : en
Publisher: World Scientific
Release Date : 2003-08-04
Progress In Analysis Proceedings Of The 3rd Isaac Congress In 2 Volumes written by Heinrich G W Begehr and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-04 with Mathematics categories.
The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.