Global Bifurcation Theory and Hilbert's Sixteenth Problem:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
2003
|
| Schriftenreihe: | Mathematics and Its Applications
562 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk "Mathematical problems" at the Second International 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 mathematics 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 coefficients 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 originated 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 possible complete information on the qualitative behaviour of integral curves defined by this equation (176] |
| Beschreibung: | 1 Online-Ressource (XXII, 182 p) |
| ISBN: | 9781441991683 9781461348191 |
| DOI: | 10.1007/978-1-4419-9168-3 |
Internformat
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| 500 | |a On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk "Mathematical problems" at the Second International 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 mathematics 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 coefficients 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 originated 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 possible complete information on the qualitative behaviour of integral curves defined by this equation (176] | ||
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Datensatz im Suchindex
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| spelling | Gaiko, Valery A. Verfasser aut Global Bifurcation Theory and Hilbert's Sixteenth Problem by Valery A. Gaiko Boston, MA Springer US 2003 1 Online-Ressource (XXII, 182 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 562 On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk "Mathematical problems" at the Second International 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 mathematics 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 coefficients 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 originated 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 possible complete information on the qualitative behaviour of integral curves defined by this equation (176] Mathematics Global analysis Differential Equations Ordinary Differential Equations Global Analysis and Analysis on Manifolds Mathematical Modeling and Industrial Mathematics Applications of Mathematics Mathematical and Computational Biology Mathematik Hilbertsches Problem 16 (DE-588)4391597-8 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 s Hilbertsches Problem 16 (DE-588)4391597-8 s 1\p DE-604 Mathematics and Its Applications 562 (DE-604)BV008163334 562 https://doi.org/10.1007/978-1-4419-9168-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gaiko, Valery A. Global Bifurcation Theory and Hilbert's Sixteenth Problem Mathematics and Its Applications Mathematics Global analysis Differential Equations Ordinary Differential Equations Global Analysis and Analysis on Manifolds Mathematical Modeling and Industrial Mathematics Applications of Mathematics Mathematical and Computational Biology Mathematik Hilbertsches Problem 16 (DE-588)4391597-8 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd |
| subject_GND | (DE-588)4391597-8 (DE-588)4078889-1 |
| title | Global Bifurcation Theory and Hilbert's Sixteenth Problem |
| title_auth | Global Bifurcation Theory and Hilbert's Sixteenth Problem |
| title_exact_search | Global Bifurcation Theory and Hilbert's Sixteenth Problem |
| title_full | Global Bifurcation Theory and Hilbert's Sixteenth Problem by Valery A. Gaiko |
| title_fullStr | Global Bifurcation Theory and Hilbert's Sixteenth Problem by Valery A. Gaiko |
| title_full_unstemmed | Global Bifurcation Theory and Hilbert's Sixteenth Problem by Valery A. Gaiko |
| title_short | Global Bifurcation Theory and Hilbert's Sixteenth Problem |
| title_sort | global bifurcation theory and hilbert s sixteenth problem |
| topic | Mathematics Global analysis Differential Equations Ordinary Differential Equations Global Analysis and Analysis on Manifolds Mathematical Modeling and Industrial Mathematics Applications of Mathematics Mathematical and Computational Biology Mathematik Hilbertsches Problem 16 (DE-588)4391597-8 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd |
| topic_facet | Mathematics Global analysis Differential Equations Ordinary Differential Equations Global Analysis and Analysis on Manifolds Mathematical Modeling and Industrial Mathematics Applications of Mathematics Mathematical and Computational Biology Mathematik Hilbertsches Problem 16 Verzweigung Mathematik |
| url | https://doi.org/10.1007/978-1-4419-9168-3 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT gaikovalerya globalbifurcationtheoryandhilbertssixteenthproblem |