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    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
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Global Bifurcation Theory and Hilbert's Sixteenth Problem

Global Bifurcation Theory and Hilbert's Sixteenth Problem

Gaiko, V.

Paperback

Series: Mathematics and Its Applications, Book 562

General Mathematics

ISBN10: 1461348196
ISBN13: 9781461348191
Publisher: Springer Nature
Published: Nov 22 2013
Pages: 182
Weight: 0.66
Height: 0.44 Width: 6.14 Depth: 9.21
Language: English
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].

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