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Global Bifurcation Theory and Hilbert's Sixteenth Problem

Global Bifurcation Theory and Hilbert's Sixteenth Problem

          
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About the Book

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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Product Details
  • ISBN-13: 9781402075711
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: 2003 ed.
  • Language: English
  • Returnable: N
  • Spine Width: 17 mm
  • Width: 158 mm
  • ISBN-10: 1402075715
  • Publisher Date: 30 Sep 2003
  • Binding: Hardback
  • Height: 248 mm
  • No of Pages: 182
  • Series Title: Mathematics and Its Applications
  • Weight: 471 gr


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