Author: S. YakovenkoPublisher: American Mathematical Soc.
ISBN: 9780821803622
Category : Differential equations
Languages : en
Pages : 244
Book Description
Concerning the Hilbert 16th Problem
Author: S. YakovenkoPublisher: American Mathematical Soc.
ISBN: 9780821803622
Category : Differential equations
Languages : en
Pages : 244
Book Description
Concerning the Hilbert 16th Problem
Author: I︠U︡. S. Ilʹi︠a︡shenkoPublisher:
ISBN: 9781470433765
Category : Electronic books
Languages : en
Pages :
Book Description
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.
Concerning the Hilbert 16th Problem
Author: Publisher: American Mathematical Society(RI)
ISBN: 9780821803622
Category :
Languages : en
Pages : 219
Book Description
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 qualitative theory of ordinary differential equations and dynamical systems.
Nine Papers on Hilbert's 16th Problem
Author: Dmitri_ Andreevich Gudkov G. A. UtkinPublisher: American Mathematical Soc.
ISBN: 9780821895504
Category : Curves, Algebraic
Languages : en
Pages : 182
Book Description
Translations of articles on mathematics appearing in various Russian mathematical serials.
Nine Papers on Hilbert's 16th Problem
Author: Dmitriĭ Andreevich GudkovPublisher: American Mathematical Soc.
ISBN:
Category : Mathematics
Languages : en
Pages : 184
Book Description
The Stokes Phenomenon And Hilbert's 16th Problem
Author: B L J BraaksmaPublisher: World Scientific
ISBN: 9814548081
Category :
Languages : en
Pages : 342
Book Description
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.
On Hilbert's 16th Problem
Author: Marian MureşanGlobal Bifurcation Theory and Hilbert's Sixteenth Problem
Author: Valery GaikoPublisher:
ISBN: 9781441991690
Category :
Languages : en
Pages : 208
Book Description
Global Bifurcation Theory and Hilbert’s Sixteenth Problem
Author: V. GaikoPublisher: Springer Science & Business Media
ISBN: 1441991689
Category : Mathematics
Languages : en
Pages : 199
Book Description
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].
Polynomial Systems and Number of Limit Cycles in Hilbert 16th Problem
Author: Amjad Islam PitafiPublisher: LAP Lambert Academic Publishing
ISBN: 9783659157097
Category :
Languages : en
Pages : 84
Book Description
In the last twenty years, the work was done on the different problems related to the Qualitative Theory of differential equations. But during the last few years, the interest surrounded around the well-known Hilbert's Sixteenth Problem which he posed at Paris Conference of International Congress of Mathematicians in 1900, together with other twenty-two problems [17]. In this book we are mainly concerned in the second part of Hilbert's sixteenth Problem, which poses the question of maximal number and relative position of limit cycles of the polynomial system of the form: (A) in which P and Q are polynomials in x and y. We write the system A in the form of (B) Where, and, are homogeneous quadratic and cubic polynomials in x and y. Chapter No. 1 comprises the basic concepts for general theory of limit cycles and Hilbert's Sixteenth Problem. Chapter No. 2 contains an Algorithm for determining so called focal basis. This can be implemented on the computer to get the estimate for the number of small-amplitude limit cycles. Chapter No. 3 deals with some classes of system (B) with several small-amplitude limit cycles.